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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Ravi, R"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" 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is-link">Go</button> </div> </div> </form> </div> </div> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Ravi%2C+R&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Ravi%2C+R&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Ravi%2C+R&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> </nav> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.18535">arXiv:2410.18535</a> <span> [<a href="https://arxiv.org/pdf/2410.18535">pdf</a>, <a href="https://arxiv.org/format/2410.18535">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Putting Off the Catching Up: Online Joint Replenishment Problem with Holding and Backlog Costs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Moseley%2C+B">Benjamin Moseley</a>, <a href="/search/cs?searchtype=author&query=Niaparast%2C+A">Aidin Niaparast</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.18535v1-abstract-short" style="display: inline;"> We study an online generalization of the classic Joint Replenishment Problem (JRP) that models the trade-off between ordering costs, holding costs, and backlog costs in supply chain planning systems. A retailer places orders to a supplier for multiple items over time: each request is for some item that the retailer needs in the future, and has an arrival time and a soft deadline. If a request is s… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.18535v1-abstract-full').style.display = 'inline'; document.getElementById('2410.18535v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.18535v1-abstract-full" style="display: none;"> We study an online generalization of the classic Joint Replenishment Problem (JRP) that models the trade-off between ordering costs, holding costs, and backlog costs in supply chain planning systems. A retailer places orders to a supplier for multiple items over time: each request is for some item that the retailer needs in the future, and has an arrival time and a soft deadline. If a request is served before its deadline, the retailer pays a holding cost per unit of the item until the deadline. However, if a request is served after its deadline, the retailer pays a backlog cost per unit. Each service incurs a fixed joint service cost and a fixed item-dependent cost for every item included in a service. These fixed costs are the same irrespective of the units of each item ordered. The goal is to schedule services to satisfy all the online requests while minimizing the sum of the service costs, the holding costs, and the backlog costs. Constant competitive online algorithms have been developed for two special cases: the make-to-order version when the deadlines are equal to arrival times (Buchbinder et al., 2013), and the make-to-stock version with hard deadlines with zero holding costs (Bienkowski et al., 2014). Our general model with holding and backlog costs has not been investigated earlier, and no online algorithms are known even in the make-to-stock version with hard deadlines and non-zero holding costs. We develop a new online algorithm for the general version of online JRP with both holding and backlog costs and establish that it is 30-competitive. Along the way, we develop a 3-competitive algorithm for the single-item case that we build on to get our final result. Our algorithm uses a greedy strategy and its competitiveness is shown using a dual fitting analysis. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.18535v1-abstract-full').style.display = 'none'; document.getElementById('2410.18535v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.01048">arXiv:2410.01048</a> <span> [<a href="https://arxiv.org/pdf/2410.01048">pdf</a>, <a href="https://arxiv.org/format/2410.01048">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> The Telephone $k$-Multicast Problem </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Hathcock%2C+D">Daniel Hathcock</a>, <a href="/search/cs?searchtype=author&query=Kortsarz%2C+G">Guy Kortsarz</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.01048v1-abstract-short" style="display: inline;"> We consider minimum time multicasting problems in directed and undirected graphs: given a root node and a subset of $t$ terminal nodes, multicasting seeks to find the minimum number of rounds within which all terminals can be informed with a message originating at the root. In each round, the telephone model we study allows the information to move via a matching from the informed nodes to the unin… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.01048v1-abstract-full').style.display = 'inline'; document.getElementById('2410.01048v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.01048v1-abstract-full" style="display: none;"> We consider minimum time multicasting problems in directed and undirected graphs: given a root node and a subset of $t$ terminal nodes, multicasting seeks to find the minimum number of rounds within which all terminals can be informed with a message originating at the root. In each round, the telephone model we study allows the information to move via a matching from the informed nodes to the uninformed nodes. Since minimum time multicasting in digraphs is poorly understood compared to the undirected variant, we study an intermediate problem in undirected graphs that specifies a target $k < t$, and requires the only $k$ of the terminals be informed in the minimum number of rounds. For this problem, we improve implications of prior results and obtain an $\tilde{O}(t^{1/3})$ multiplicative approximation. For the directed version, we obtain an {\em additive} $\tilde{O}(k^{1/2})$ approximation algorithm (with a poly-logarithmic multiplicative factor). Our algorithms are based on reductions to the related problems of finding $k$-trees of minimum poise (sum of maximum degree and diameter) and applying a combination of greedy network decomposition techniques and set covering under partition matroid constraints. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.01048v1-abstract-full').style.display = 'none'; document.getElementById('2410.01048v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">@APPROX24</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 68W25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.01268">arXiv:2408.01268</a> <span> [<a href="https://arxiv.org/pdf/2408.01268">pdf</a>, <a href="https://arxiv.org/format/2408.01268">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> Rumour Spreading Depends on the Latent Geometry and Degree Distribution in Social Network Models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Kaufmann%2C+M">Marc Kaufmann</a>, <a href="/search/cs?searchtype=author&query=Lakis%2C+K">Kostas Lakis</a>, <a href="/search/cs?searchtype=author&query=Lengler%2C+J">Johannes Lengler</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R+R">Raghu Raman Ravi</a>, <a href="/search/cs?searchtype=author&query=Schaller%2C+U">Ulysse Schaller</a>, <a href="/search/cs?searchtype=author&query=Sturm%2C+K">Konstantin Sturm</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.01268v2-abstract-short" style="display: inline;"> We study push-pull rumour spreading in small-world models for social networks where the degrees follow a power-law. In a non-geometric setting Fountoulakis, Panagiotou and Sauerwald have shown that rumours always spread fast (SODA 2012). On the other hand, Janssen and Mehrabian have found that rumours spread slowly in a spatial preferential attachment model (SIDMA 2017). We study the question syst… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.01268v2-abstract-full').style.display = 'inline'; document.getElementById('2408.01268v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.01268v2-abstract-full" style="display: none;"> We study push-pull rumour spreading in small-world models for social networks where the degrees follow a power-law. In a non-geometric setting Fountoulakis, Panagiotou and Sauerwald have shown that rumours always spread fast (SODA 2012). On the other hand, Janssen and Mehrabian have found that rumours spread slowly in a spatial preferential attachment model (SIDMA 2017). We study the question systematically for the model of geometric inhomogeneous random graphs (GIRGs), which has been found to be a good theoretical and empirical fit for social networks. Our result is two-fold: with classical Euclidean geometry both slow and fast rumour spreading may occur, depending on the exponent of the power law and the prevalence of weak ties in the networks, and we fully characterise the phase boundaries between those two regimes. Depending on the parameters, fast spreading may either mean polylogarithmic time or even doubly logarithmic time. Secondly, we show that rumour spreading is always fast in a non-metric geometry. The considered non-metric geometry allows to model social connections where resemblance of vertices in a single attribute, such as familial kinship, already strongly indicates the presence of an edge. Classical Euclidean Geometry fails to capture such ties. For some regimes in the Euclidean setting, the efficient pathways for spreading rumours differ from previously identified paths. A vertex of degree $d$ can transmit the rumour efficiently to a vertex of larger degree by a chain of length $3$, where one of the two intermediaries has constant degree, and the other has degree $d^{c}$ for some constant $c<1$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.01268v2-abstract-full').style.display = 'none'; document.getElementById('2408.01268v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">40 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 05C82; 91D25; 91D30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.13909">arXiv:2407.13909</a> <span> [<a href="https://arxiv.org/pdf/2407.13909">pdf</a>, <a href="https://arxiv.org/format/2407.13909">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Retrieval">cs.IR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> </div> </div> <p class="title is-5 mathjax"> PRAGyan -- Connecting the Dots in Tweets </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Ravi%2C+R">Rahul Ravi</a>, <a href="/search/cs?searchtype=author&query=Ginde%2C+G">Gouri Ginde</a>, <a href="/search/cs?searchtype=author&query=Rokne%2C+J">Jon Rokne</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2407.13909v1-abstract-short" style="display: inline;"> As social media platforms grow, understanding the underlying reasons behind events and statements becomes crucial for businesses, policymakers, and researchers. This research explores the integration of Knowledge Graphs (KGs) with Large Language Models (LLMs) to perform causal analysis of tweets dataset. The LLM aided analysis techniques often lack depth in uncovering the causes driving observed e… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.13909v1-abstract-full').style.display = 'inline'; document.getElementById('2407.13909v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.13909v1-abstract-full" style="display: none;"> As social media platforms grow, understanding the underlying reasons behind events and statements becomes crucial for businesses, policymakers, and researchers. This research explores the integration of Knowledge Graphs (KGs) with Large Language Models (LLMs) to perform causal analysis of tweets dataset. The LLM aided analysis techniques often lack depth in uncovering the causes driving observed effects. By leveraging KGs and LLMs, which encode rich semantic relationships and temporal information, this study aims to uncover the complex interplay of factors influencing causal dynamics and compare the results obtained using GPT-3.5 Turbo. We employ a Retrieval-Augmented Generation (RAG) model, utilizing a KG stored in a Neo4j (a.k.a PRAGyan) data format, to retrieve relevant context for causal reasoning. Our approach demonstrates that the KG-enhanced LLM RAG can provide improved results when compared to the baseline LLM (GPT-3.5 Turbo) model as the source corpus increases in size. Our qualitative analysis highlights the advantages of combining KGs with LLMs for improved interpretability and actionable insights, facilitating informed decision-making across various domains. Whereas, quantitative analysis using metrics such as BLEU and cosine similarity show that our approach outperforms the baseline by 10\%. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.13909v1-abstract-full').style.display = 'none'; document.getElementById('2407.13909v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, ASONAM</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.19369">arXiv:2405.19369</a> <span> [<a href="https://arxiv.org/pdf/2405.19369">pdf</a>, <a href="https://arxiv.org/format/2405.19369">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Metric Geometry">math.MG</span> </div> </div> <p class="title is-5 mathjax"> Sublinear Cuts are the Exception in BDF-GIRGs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Kaufmann%2C+M">Marc Kaufmann</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R+R">Raghu Raman Ravi</a>, <a href="/search/cs?searchtype=author&query=Schaller%2C+U">Ulysse Schaller</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2405.19369v1-abstract-short" style="display: inline;"> The introduction of geometry has proven instrumental in the efforts towards more realistic models for real-world networks. In Geometric Inhomogeneous Random Graphs (GIRGs), Euclidean Geometry induces clustering of the vertices, which is widely observed in networks in the wild. Euclidean Geometry in multiple dimensions however restricts proximity of vertices to those cases where vertices are close… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.19369v1-abstract-full').style.display = 'inline'; document.getElementById('2405.19369v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.19369v1-abstract-full" style="display: none;"> The introduction of geometry has proven instrumental in the efforts towards more realistic models for real-world networks. In Geometric Inhomogeneous Random Graphs (GIRGs), Euclidean Geometry induces clustering of the vertices, which is widely observed in networks in the wild. Euclidean Geometry in multiple dimensions however restricts proximity of vertices to those cases where vertices are close in each coordinate. We introduce a large class of GIRG extensions, called BDF-GIRGs, which capture arbitrary hierarchies of the coordinates within the distance function of the vertex feature space. These distance functions have the potential to allow more realistic modeling of the complex formation of social ties in real-world networks, where similarities between people lead to connections. Here, similarity with respect to certain features, such as familial kinship or a shared workplace, suffices for the formation of ties. It is known that - while many key properties of GIRGs, such as log-log average distance and sparsity, are independent of the distance function - the Euclidean metric induces small separators, i.e. sublinear cuts of the unique giant component in GIRGs, whereas no such sublinear separators exist under the component-wise minimum distance. Building on work of Lengler and Todorovi膰, we give a complete classification for the existence of small separators in BDF-GIRGs. We further show that BDF-GIRGs all fulfill a stochastic triangle inequality and thus also exhibit clustering. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.19369v1-abstract-full').style.display = 'none'; document.getElementById('2405.19369v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.05815">arXiv:2403.05815</a> <span> [<a href="https://arxiv.org/pdf/2403.05815">pdf</a>, <a href="https://arxiv.org/format/2403.05815">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Robotics">cs.RO</span> </div> </div> <p class="title is-5 mathjax"> N-QR: Natural Quick Response Codes for Multi-Robot Instance Correspondence </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Glaser%2C+N+M">Nathaniel Moore Glaser</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">Rajashree Ravi</a>, <a href="/search/cs?searchtype=author&query=Kira%2C+Z">Zsolt Kira</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.05815v1-abstract-short" style="display: inline;"> Image correspondence serves as the backbone for many tasks in robotics, such as visual fusion, localization, and mapping. However, existing correspondence methods do not scale to large multi-robot systems, and they struggle when image features are weak, ambiguous, or evolving. In response, we propose Natural Quick Response codes, or N-QR, which enables rapid and reliable correspondence between lar… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.05815v1-abstract-full').style.display = 'inline'; document.getElementById('2403.05815v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.05815v1-abstract-full" style="display: none;"> Image correspondence serves as the backbone for many tasks in robotics, such as visual fusion, localization, and mapping. However, existing correspondence methods do not scale to large multi-robot systems, and they struggle when image features are weak, ambiguous, or evolving. In response, we propose Natural Quick Response codes, or N-QR, which enables rapid and reliable correspondence between large-scale teams of heterogeneous robots. Our method works like a QR code, using keypoint-based alignment, rapid encoding, and error correction via ensembles of image patches of natural patterns. We deploy our algorithm in a production-scale robotic farm, where groups of growing plants must be matched across many robots. We demonstrate superior performance compared to several baselines, obtaining a retrieval accuracy of 88.2%. Our method generalizes to a farm with 100 robots, achieving a 12.5x reduction in bandwidth and a 20.5x speedup. We leverage our method to correspond 700k plants and confirm a link between a robotic seeding policy and germination. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.05815v1-abstract-full').style.display = 'none'; document.getElementById('2403.05815v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">IEEE International Conference on Robotics and Automation (ICRA), 2024</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.13853">arXiv:2401.13853</a> <span> [<a href="https://arxiv.org/pdf/2401.13853">pdf</a>, <a href="https://arxiv.org/format/2401.13853">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Robotics">cs.RO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> </div> </div> <p class="title is-5 mathjax"> Dataset and Benchmark: Novel Sensors for Autonomous Vehicle Perception </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Carmichael%2C+S">Spencer Carmichael</a>, <a href="/search/cs?searchtype=author&query=Buchan%2C+A">Austin Buchan</a>, <a href="/search/cs?searchtype=author&query=Ramanagopal%2C+M">Mani Ramanagopal</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">Radhika Ravi</a>, <a href="/search/cs?searchtype=author&query=Vasudevan%2C+R">Ram Vasudevan</a>, <a href="/search/cs?searchtype=author&query=Skinner%2C+K+A">Katherine A. Skinner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.13853v1-abstract-short" style="display: inline;"> Conventional cameras employed in autonomous vehicle (AV) systems support many perception tasks, but are challenged by low-light or high dynamic range scenes, adverse weather, and fast motion. Novel sensors, such as event and thermal cameras, offer capabilities with the potential to address these scenarios, but they remain to be fully exploited. This paper introduces the Novel Sensors for Autonomou… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.13853v1-abstract-full').style.display = 'inline'; document.getElementById('2401.13853v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.13853v1-abstract-full" style="display: none;"> Conventional cameras employed in autonomous vehicle (AV) systems support many perception tasks, but are challenged by low-light or high dynamic range scenes, adverse weather, and fast motion. Novel sensors, such as event and thermal cameras, offer capabilities with the potential to address these scenarios, but they remain to be fully exploited. This paper introduces the Novel Sensors for Autonomous Vehicle Perception (NSAVP) dataset to facilitate future research on this topic. The dataset was captured with a platform including stereo event, thermal, monochrome, and RGB cameras as well as a high precision navigation system providing ground truth poses. The data was collected by repeatedly driving two ~8 km routes and includes varied lighting conditions and opposing viewpoint perspectives. We provide benchmarking experiments on the task of place recognition to demonstrate challenges and opportunities for novel sensors to enhance critical AV perception tasks. To our knowledge, the NSAVP dataset is the first to include stereo thermal cameras together with stereo event and monochrome cameras. The dataset and supporting software suite is available at: https://umautobots.github.io/nsavp <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.13853v1-abstract-full').style.display = 'none'; document.getElementById('2401.13853v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Under review</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.00013">arXiv:2401.00013</a> <span> [<a href="https://arxiv.org/pdf/2401.00013">pdf</a>, <a href="https://arxiv.org/format/2401.00013">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Databases">cs.DB</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> HITSnDIFFs: From Truth Discovery to Ability Discovery by Recovering Matrices with the Consecutive Ones Property </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Chen%2C+Z">Zixuan Chen</a>, <a href="/search/cs?searchtype=author&query=Mitra%2C+S">Subhodeep Mitra</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R Ravi</a>, <a href="/search/cs?searchtype=author&query=Gatterbauer%2C+W">Wolfgang Gatterbauer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.00013v1-abstract-short" style="display: inline;"> We analyze a general problem in a crowd-sourced setting where one user asks a question (also called item) and other users return answers (also called labels) for this question. Different from existing crowd sourcing work which focuses on finding the most appropriate label for the question (the "truth"), our problem is to determine a ranking of the users based on their ability to answer questions.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.00013v1-abstract-full').style.display = 'inline'; document.getElementById('2401.00013v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.00013v1-abstract-full" style="display: none;"> We analyze a general problem in a crowd-sourced setting where one user asks a question (also called item) and other users return answers (also called labels) for this question. Different from existing crowd sourcing work which focuses on finding the most appropriate label for the question (the "truth"), our problem is to determine a ranking of the users based on their ability to answer questions. We call this problem "ability discovery" to emphasize the connection to and duality with the more well-studied problem of "truth discovery". To model items and their labels in a principled way, we draw upon Item Response Theory (IRT) which is the widely accepted theory behind standardized tests such as SAT and GRE. We start from an idealized setting where the relative performance of users is consistent across items and better users choose better fitting labels for each item. We posit that a principled algorithmic solution to our more general problem should solve this ideal setting correctly and observe that the response matrices in this setting obey the Consecutive Ones Property (C1P). While C1P is well understood algorithmically with various discrete algorithms, we devise a novel variant of the HITS algorithm which we call "HITSNDIFFS" (or HND), and prove that it can recover the ideal C1P-permutation in case it exists. Unlike fast combinatorial algorithms for finding the consecutive ones permutation (if it exists), HND also returns an ordering when such a permutation does not exist. Thus it provides a principled heuristic for our problem that is guaranteed to return the correct answer in the ideal setting. Our experiments show that HND produces user rankings with robustly high accuracy compared to state-of-the-art truth discovery methods. We also show that our novel variant of HITS scales better in the number of users than ABH, the only prior spectral C1P reconstruction algorithm. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.00013v1-abstract-full').style.display = 'none'; document.getElementById('2401.00013v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 14 figures, long version of of ICDE 2024 conference paper</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.15357">arXiv:2312.15357</a> <span> [<a href="https://arxiv.org/pdf/2312.15357">pdf</a>, <a href="https://arxiv.org/format/2312.15357">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">stat.ML</span> </div> </div> <p class="title is-5 mathjax"> Optimal Decision Tree and Adaptive Submodular Ranking with Noisy Outcomes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Jia%2C+S">Su Jia</a>, <a href="/search/cs?searchtype=author&query=Navidi%2C+F">Fatemeh Navidi</a>, <a href="/search/cs?searchtype=author&query=Nagarajan%2C+V">Viswanath Nagarajan</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.15357v2-abstract-short" style="display: inline;"> In pool-based active learning, the learner is given an unlabeled data set and aims to efficiently learn the unknown hypothesis by querying the labels of the data points. This can be formulated as the classical Optimal Decision Tree (ODT) problem: Given a set of tests, a set of hypotheses, and an outcome for each pair of test and hypothesis, our objective is to find a low-cost testing procedure (i.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.15357v2-abstract-full').style.display = 'inline'; document.getElementById('2312.15357v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.15357v2-abstract-full" style="display: none;"> In pool-based active learning, the learner is given an unlabeled data set and aims to efficiently learn the unknown hypothesis by querying the labels of the data points. This can be formulated as the classical Optimal Decision Tree (ODT) problem: Given a set of tests, a set of hypotheses, and an outcome for each pair of test and hypothesis, our objective is to find a low-cost testing procedure (i.e., decision tree) that identifies the true hypothesis. This optimization problem has been extensively studied under the assumption that each test generates a deterministic outcome. However, in numerous applications, for example, clinical trials, the outcomes may be uncertain, which renders the ideas from the deterministic setting invalid. In this work, we study a fundamental variant of the ODT problem in which some test outcomes are noisy, even in the more general case where the noise is persistent, i.e., repeating a test gives the same noisy output. Our approximation algorithms provide guarantees that are nearly best possible and hold for the general case of a large number of noisy outcomes per test or per hypothesis where the performance degrades continuously with this number. We numerically evaluated our algorithms for identifying toxic chemicals and learning linear classifiers, and observed that our algorithms have costs very close to the information-theoretic minimum. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.15357v2-abstract-full').style.display = 'none'; document.getElementById('2312.15357v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.15356">arXiv:2312.15356</a> <span> [<a href="https://arxiv.org/pdf/2312.15356">pdf</a>, <a href="https://arxiv.org/format/2312.15356">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">stat.ML</span> </div> </div> <p class="title is-5 mathjax"> Short-lived High-volume Multi-A(rmed)/B(andits) Testing </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Jia%2C+S">Su Jia</a>, <a href="/search/cs?searchtype=author&query=Li%2C+A">Andrew Li</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Oli%2C+N">Nishant Oli</a>, <a href="/search/cs?searchtype=author&query=Duff%2C+P">Paul Duff</a>, <a href="/search/cs?searchtype=author&query=Anderson%2C+I">Ian Anderson</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.15356v1-abstract-short" style="display: inline;"> Modern platforms leverage randomized experiments to make informed decisions from a given set of items (``treatments''). As a particularly challenging scenario, these items may (i) arrive in high volume, with thousands of new items being released per hour, and (ii) have short lifetime, say, due to the item's transient nature or underlying non-stationarity that impels the platform to perceive the sa… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.15356v1-abstract-full').style.display = 'inline'; document.getElementById('2312.15356v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.15356v1-abstract-full" style="display: none;"> Modern platforms leverage randomized experiments to make informed decisions from a given set of items (``treatments''). As a particularly challenging scenario, these items may (i) arrive in high volume, with thousands of new items being released per hour, and (ii) have short lifetime, say, due to the item's transient nature or underlying non-stationarity that impels the platform to perceive the same item as distinct copies over time. Thus motivated, we study a Bayesian multiple-play bandit problem that encapsulates the key features of the multivariate testing (or ``multi-A/B testing'') problem with a high volume of short-lived arms. In each round, a set of $k$ arms arrive, each available for $w$ rounds. Without knowing the mean reward for each arm, the learner selects a multiset of $n$ arms and immediately observes their realized rewards. We aim to minimize the loss due to not knowing the mean rewards, averaged over instances generated from a given prior distribution. We show that when $k = O(n^蟻)$ for some constant $蟻>0$, our proposed policy has $\tilde O(n^{-\min \{蟻, \frac 12 (1+\frac 1w)^{-1}\}})$ loss on a sufficiently large class of prior distributions. We complement this result by showing that every policy suffers $惟(n^{-\min \{蟻, \frac 12\}})$ loss on the same class of distributions. We further validate the effectiveness of our policy through a large-scale field experiment on {\em Glance}, a content-card-serving platform that faces exactly the above challenge. A simple variant of our policy outperforms the platform's current recommender by 4.32\% in total duration and 7.48\% in total number of click-throughs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.15356v1-abstract-full').style.display = 'none'; document.getElementById('2312.15356v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.15286">arXiv:2312.15286</a> <span> [<a href="https://arxiv.org/pdf/2312.15286">pdf</a>, <a href="https://arxiv.org/format/2312.15286">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Science and Game Theory">cs.GT</span> </div> </div> <p class="title is-5 mathjax"> Markdown Pricing Under an Unknown Parametric Demand Model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Jia%2C+S">Su Jia</a>, <a href="/search/cs?searchtype=author&query=Li%2C+A">Andrew Li</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.15286v1-abstract-short" style="display: inline;"> Consider a single-product revenue-maximization problem where the seller monotonically decreases the price in $n$ rounds with an unknown demand model coming from a given family. Without monotonicity, the minimax regret is $\tilde O(n^{2/3})$ for the Lipschitz demand family and $\tilde O(n^{1/2})$ for a general class of parametric demand models. With monotonicity, the minimax regret is… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.15286v1-abstract-full').style.display = 'inline'; document.getElementById('2312.15286v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.15286v1-abstract-full" style="display: none;"> Consider a single-product revenue-maximization problem where the seller monotonically decreases the price in $n$ rounds with an unknown demand model coming from a given family. Without monotonicity, the minimax regret is $\tilde O(n^{2/3})$ for the Lipschitz demand family and $\tilde O(n^{1/2})$ for a general class of parametric demand models. With monotonicity, the minimax regret is $\tilde O(n^{3/4})$ if the revenue function is Lipschitz and unimodal. However, the minimax regret for parametric families remained open. In this work, we provide a complete settlement for this fundamental problem. We introduce the crossing number to measure the complexity of a family of demand functions. In particular, the family of degree-$k$ polynomials has a crossing number $k$. Based on conservatism under uncertainty, we present (i) a policy with an optimal $螛(\log^2 n)$ regret for families with crossing number $k=0$, and (ii) another policy with an optimal $\tilde 螛(n^{k/(k+1)})$ regret when $k\ge 1$. These bounds are asymptotically higher than the $\tilde O(\log n)$ and $\tilde 螛(\sqrt n)$ minimax regret for the same families without the monotonicity constraint. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.15286v1-abstract-full').style.display = 'none'; document.getElementById('2312.15286v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.08665">arXiv:2209.08665</a> <span> [<a href="https://arxiv.org/pdf/2209.08665">pdf</a>, <a href="https://arxiv.org/format/2209.08665">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Human-Computer Interaction">cs.HC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> Allocation Schemes in Analytic Evaluation: Applicant-Centric Holistic or Attribute-Centric Segmented? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Wang%2C+J">Jingyan Wang</a>, <a href="/search/cs?searchtype=author&query=Baharav%2C+C">Carmel Baharav</a>, <a href="/search/cs?searchtype=author&query=Shah%2C+N+B">Nihar B. Shah</a>, <a href="/search/cs?searchtype=author&query=Woolley%2C+A+W">Anita Williams Woolley</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.08665v1-abstract-short" style="display: inline;"> Many applications such as hiring and university admissions involve evaluation and selection of applicants. These tasks are fundamentally difficult, and require combining evidence from multiple different aspects (what we term "attributes"). In these applications, the number of applicants is often large, and a common practice is to assign the task to multiple evaluators in a distributed fashion. Spe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.08665v1-abstract-full').style.display = 'inline'; document.getElementById('2209.08665v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.08665v1-abstract-full" style="display: none;"> Many applications such as hiring and university admissions involve evaluation and selection of applicants. These tasks are fundamentally difficult, and require combining evidence from multiple different aspects (what we term "attributes"). In these applications, the number of applicants is often large, and a common practice is to assign the task to multiple evaluators in a distributed fashion. Specifically, in the often-used holistic allocation, each evaluator is assigned a subset of the applicants, and is asked to assess all relevant information for their assigned applicants. However, such an evaluation process is subject to issues such as miscalibration (evaluators see only a small fraction of the applicants and may not get a good sense of relative quality), and discrimination (evaluators are influenced by irrelevant information about the applicants). We identify that such attribute-based evaluation allows alternative allocation schemes. Specifically, we consider assigning each evaluator more applicants but fewer attributes per applicant, termed segmented allocation. We compare segmented allocation to holistic allocation on several dimensions via theoretical and experimental methods. We establish various tradeoffs between these two approaches, and identify conditions under which one approach results in more accurate evaluation than the other. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.08665v1-abstract-full').style.display = 'none'; document.getElementById('2209.08665v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.05471">arXiv:2209.05471</a> <span> [<a href="https://arxiv.org/pdf/2209.05471">pdf</a>, <a href="https://arxiv.org/format/2209.05471">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computers and Society">cs.CY</span> </div> </div> <p class="title is-5 mathjax"> PATE: Property, Amenities, Traffic and Emotions Coming Together for Real Estate Price Prediction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Zhao%2C+Y">Yaping Zhao</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">Ramgopal Ravi</a>, <a href="/search/cs?searchtype=author&query=Shi%2C+S">Shuhui Shi</a>, <a href="/search/cs?searchtype=author&query=Wang%2C+Z">Zhongrui Wang</a>, <a href="/search/cs?searchtype=author&query=Lam%2C+E+Y">Edmund Y. Lam</a>, <a href="/search/cs?searchtype=author&query=Zhao%2C+J">Jichang Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.05471v2-abstract-short" style="display: inline;"> Real estate prices have a significant impact on individuals, families, businesses, and governments. The general objective of real estate price prediction is to identify and exploit socioeconomic patterns arising from real estate transactions over multiple aspects, ranging from the property itself to other contributing factors. However, price prediction is a challenging multidimensional problem tha… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.05471v2-abstract-full').style.display = 'inline'; document.getElementById('2209.05471v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.05471v2-abstract-full" style="display: none;"> Real estate prices have a significant impact on individuals, families, businesses, and governments. The general objective of real estate price prediction is to identify and exploit socioeconomic patterns arising from real estate transactions over multiple aspects, ranging from the property itself to other contributing factors. However, price prediction is a challenging multidimensional problem that involves estimating many characteristics beyond the property itself. In this paper, we use multiple sources of data to evaluate the economic contribution of different socioeconomic characteristics such as surrounding amenities, traffic conditions and social emotions. Our experiments were conducted on 28,550 houses in Beijing, China and we rank each characteristic by its importance. Since the use of multi-source information improves the accuracy of predictions, the aforementioned characteristics can be an invaluable resource to assess the economic and social value of real estate. Code and data are available at: https://github.com/IndigoPurple/PATE <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.05471v2-abstract-full').style.display = 'none'; document.getElementById('2209.05471v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted by IEEE DSAA 2022. 10 pages, 3 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.12542">arXiv:2208.12542</a> <span> [<a href="https://arxiv.org/pdf/2208.12542">pdf</a>, <a href="https://arxiv.org/format/2208.12542">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computers and Society">cs.CY</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> </div> </div> <p class="title is-5 mathjax"> H4M: Heterogeneous, Multi-source, Multi-modal, Multi-view and Multi-distributional Dataset for Socioeconomic Analytics in the Case of Beijing </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Zhao%2C+Y">Yaping Zhao</a>, <a href="/search/cs?searchtype=author&query=Shi%2C+S">Shuhui Shi</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">Ramgopal Ravi</a>, <a href="/search/cs?searchtype=author&query=Wang%2C+Z">Zhongrui Wang</a>, <a href="/search/cs?searchtype=author&query=Lam%2C+E+Y">Edmund Y. Lam</a>, <a href="/search/cs?searchtype=author&query=Zhao%2C+J">Jichang Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.12542v1-abstract-short" style="display: inline;"> The study of socioeconomic status has been reformed by the availability of digital records containing data on real estate, points of interest, traffic and social media trends such as micro-blogging. In this paper, we describe a heterogeneous, multi-source, multi-modal, multi-view and multi-distributional dataset named "H4M". The mixed dataset contains data on real estate transactions, points of in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.12542v1-abstract-full').style.display = 'inline'; document.getElementById('2208.12542v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.12542v1-abstract-full" style="display: none;"> The study of socioeconomic status has been reformed by the availability of digital records containing data on real estate, points of interest, traffic and social media trends such as micro-blogging. In this paper, we describe a heterogeneous, multi-source, multi-modal, multi-view and multi-distributional dataset named "H4M". The mixed dataset contains data on real estate transactions, points of interest, traffic patterns and micro-blogging trends from Beijing, China. The unique composition of H4M makes it an ideal test bed for methodologies and approaches aimed at studying and solving problems related to real estate, traffic, urban mobility planning, social sentiment analysis etc. The dataset is available at: https://indigopurple.github.io/H4M/index.html <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.12542v1-abstract-full').style.display = 'none'; document.getElementById('2208.12542v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted by IEEE DSAA 2022. 10 pages, 10 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.07983">arXiv:2207.07983</a> <span> [<a href="https://arxiv.org/pdf/2207.07983">pdf</a>, <a href="https://arxiv.org/ps/2207.07983">ps</a>, <a href="https://arxiv.org/format/2207.07983">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Approximation algorithms for Steiner Tree Augmentation Problems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Zhang%2C+W">Weizhong Zhang</a>, <a href="/search/cs?searchtype=author&query=Zlatin%2C+M">Michael Zlatin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.07983v2-abstract-short" style="display: inline;"> In the Steiner Tree Augmentation Problem (STAP), we are given a graph $G = (V,E)$, a set of terminals $R \subseteq V$, and a Steiner tree $T$ spanning $R$. The edges $L := E \setminus E(T)$ are called links and have non-negative costs. The goal is to augment $T$ by adding a minimum cost set of links, so that there are 2 edge-disjoint paths between each pair of vertices in $R$. This problem is a sp… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.07983v2-abstract-full').style.display = 'inline'; document.getElementById('2207.07983v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.07983v2-abstract-full" style="display: none;"> In the Steiner Tree Augmentation Problem (STAP), we are given a graph $G = (V,E)$, a set of terminals $R \subseteq V$, and a Steiner tree $T$ spanning $R$. The edges $L := E \setminus E(T)$ are called links and have non-negative costs. The goal is to augment $T$ by adding a minimum cost set of links, so that there are 2 edge-disjoint paths between each pair of vertices in $R$. This problem is a special case of the Survivable Network Design Problem, which can be approximated to within a factor of 2 using iterative rounding~\cite{J2001}. We give the first polynomial time algorithm for STAP with approximation ratio better than 2. In particular, we achieve an approximation ratio of $(1.5 + \varepsilon)$. To do this, we employ the Local Search approach of~\cite{TZ2022} for the Tree Augmentation Problem and generalize their main decomposition theorem from links (of size two) to hyper-links. We also consider the Node-Weighted Steiner Tree Augmentation Problem (NW-STAP) in which the non-terminal nodes have non-negative costs. We seek a cheapest subset $S \subseteq V \setminus R$ so that $G[R \cup S]$ is 2-edge-connected. Using a result of Nutov~\cite{N2010}, there exists an $O(\log |R|)$-approximation for this problem. We provide an $O(\log^2 (|R|))$-approximation algorithm for NW-STAP using a greedy algorithm leveraging the spider decomposition of optimal solutions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.07983v2-abstract-full').style.display = 'none'; document.getElementById('2207.07983v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.04548">arXiv:2205.04548</a> <span> [<a href="https://arxiv.org/pdf/2205.04548">pdf</a>, <a href="https://arxiv.org/format/2205.04548">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Multiagent Systems">cs.MA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Robotics">cs.RO</span> </div> </div> <p class="title is-5 mathjax"> Informed Steiner Trees: Sampling and Pruning for Multi-Goal Path Finding in High Dimensions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Chandak%2C+N">Nikhil Chandak</a>, <a href="/search/cs?searchtype=author&query=Chour%2C+K">Kenny Chour</a>, <a href="/search/cs?searchtype=author&query=Rathinam%2C+S">Sivakumar Rathinam</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2205.04548v1-abstract-short" style="display: inline;"> We interleave sampling based motion planning methods with pruning ideas from minimum spanning tree algorithms to develop a new approach for solving a Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach alternates between sampling points from selected regions in the search space and de-emphasizing regions that may not lead to good solutions for MGPF. Our approach provide… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.04548v1-abstract-full').style.display = 'inline'; document.getElementById('2205.04548v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.04548v1-abstract-full" style="display: none;"> We interleave sampling based motion planning methods with pruning ideas from minimum spanning tree algorithms to develop a new approach for solving a Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach alternates between sampling points from selected regions in the search space and de-emphasizing regions that may not lead to good solutions for MGPF. Our approach provides an asymptotic, 2-approximation guarantee for MGPF. We also present extensive numerical results to illustrate the advantages of our proposed approach over uniform sampling in terms of the quality of the solutions found and computation speed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.04548v1-abstract-full').style.display = 'none'; document.getElementById('2205.04548v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.03697">arXiv:2203.03697</a> <span> [<a href="https://arxiv.org/pdf/2203.03697">pdf</a>, <a href="https://arxiv.org/ps/2203.03697">ps</a>, <a href="https://arxiv.org/format/2203.03697">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> </div> </div> <p class="title is-5 mathjax"> Unit Perturbations in Budgeted Spanning Tree Problems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Aissi%2C+H">Hassene Aissi</a>, <a href="/search/cs?searchtype=author&query=Attias%2C+S">Solal Attias</a>, <a href="/search/cs?searchtype=author&query=Chen%2C+D+Q">Da Qi Chen</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2203.03697v1-abstract-short" style="display: inline;"> The minimum spanning tree of a graph is a well-studied structure that is the basis of countless graph theoretic and optimization problem. We study the minimum spanning tree (MST) perturbation problem where the goal is to spend a fixed budget to increase the weight of edges in order to increase the weight of the MST as much as possible. Two popular models of perturbation are bulk and continuous. In… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.03697v1-abstract-full').style.display = 'inline'; document.getElementById('2203.03697v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.03697v1-abstract-full" style="display: none;"> The minimum spanning tree of a graph is a well-studied structure that is the basis of countless graph theoretic and optimization problem. We study the minimum spanning tree (MST) perturbation problem where the goal is to spend a fixed budget to increase the weight of edges in order to increase the weight of the MST as much as possible. Two popular models of perturbation are bulk and continuous. In the bulk model, the weight of any edge can be increased exactly once to some predetermined weight. In the continuous model, one can pay a fractional amount of cost to increase the weight of any edge by a proportional amount. Frederickson and Solis-Oba \cite{FS96} have studied these two models and showed that bulk perturbation for MST is as hard as the $k$-cut problem while the continuous perturbation model is solvable in poly-time. In this paper, we study an intermediate unit perturbation variation of this problem where the weight of each edge can be increased many times but at an integral unit amount every time. We provide an $(opt/2 -1)$-approximation in polynomial time where $opt$ is the optimal increase in the weight. We also study the associated dual targeted version of the problem where the goal is to increase the weight of the MST by a target amount while minimizing the cost of perturbation. We provide a $2$-approximation for this variation. Furthermore we show that assuming the Small Set Expansion Hypothesis, both problems are hard to approximate. We also point out an error in the proof provided by Frederickson and Solis-Oba in \cite{FS96} with regard to their solution to the continuous perturbation model. Although their algorithm is correct, their analysis is flawed. We provide a correct proof here. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.03697v1-abstract-full').style.display = 'none'; document.getElementById('2203.03697v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.05450">arXiv:2111.05450</a> <span> [<a href="https://arxiv.org/pdf/2111.05450">pdf</a>, <a href="https://arxiv.org/ps/2111.05450">ps</a>, <a href="https://arxiv.org/format/2111.05450">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> </div> </div> <p class="title is-5 mathjax"> Timeliness Through Telephones: Approximating Information Freshness in Vector Clock Models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Chen%2C+D+Q">Da Qi Chen</a>, <a href="/search/cs?searchtype=author&query=An%2C+L">Lin An</a>, <a href="/search/cs?searchtype=author&query=Niaparast%2C+A">Aidin Niaparast</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Rudenko%2C+O">Oleksandr Rudenko</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.05450v2-abstract-short" style="display: inline;"> We consider an information dissemination problem where the root of an undirected graph constantly updates its information. The goal is to keep every other node in the graph about the root as freshly informed as possible. Our synchronous information spreading model uses telephone calls at each time step, in which any node can call at most one neighbor, thus forming a matching over which information… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.05450v2-abstract-full').style.display = 'inline'; document.getElementById('2111.05450v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.05450v2-abstract-full" style="display: none;"> We consider an information dissemination problem where the root of an undirected graph constantly updates its information. The goal is to keep every other node in the graph about the root as freshly informed as possible. Our synchronous information spreading model uses telephone calls at each time step, in which any node can call at most one neighbor, thus forming a matching over which information is transmitted at each step. We introduce two problems in minimizing two natural objectives (Maximum and Average) of the latency of the root's information at all nodes in the network. After deriving a simple reduction from the maximum rooted latency problem to the well-studied minimum broadcast time problem, we focus on the average rooted latency version. We introduce a natural problem of finding a finite schedule that minimizes the average broadcast time from a root. We show that any average rooted latency induces a solution to this average broadcast problem within a constant factor and conversely, this average broadcast time is within a logarithmic factor of the average rooted latency. Then, by approximating the average broadcast time problem via rounding a time-indexed linear programming relaxation, we obtain a logarithmic approximation to the average latency problem. Surprisingly, we show that using the average broadcast time for average rooted latency introduces this necessary logarithmic factor overhead even in trees. We overcome this hurdle and give a 40-approximation for trees. For this, we design an algorithm to find near-optimal locally-periodic schedules in trees where each vertex receives information from its parent in regular intervals. On the other side, we show how such well-behaved schedules approximate the optimal schedule within a constant factor. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.05450v2-abstract-full').style.display = 'none'; document.getElementById('2111.05450v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.00148">arXiv:2111.00148</a> <span> [<a href="https://arxiv.org/pdf/2111.00148">pdf</a>, <a href="https://arxiv.org/format/2111.00148">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> On Small-Depth Tree Augmentations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Parekh%2C+O">Ojas Parekh</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Zlatin%2C+M">Michael Zlatin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.00148v1-abstract-short" style="display: inline;"> We study the Weighted Tree Augmentation Problem for general link costs. We show that the integrality gap of the ODD-LP relaxation for the (weighted) Tree Augmentation Problem for a $k$-level tree instance is at most $2 - \frac{1}{2^{k-1}}$. For 2- and 3-level trees, these ratios are $\frac32$ and $\frac74$ respectively. Our proofs are constructive and yield polynomial-time approximation algorithms… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.00148v1-abstract-full').style.display = 'inline'; document.getElementById('2111.00148v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.00148v1-abstract-full" style="display: none;"> We study the Weighted Tree Augmentation Problem for general link costs. We show that the integrality gap of the ODD-LP relaxation for the (weighted) Tree Augmentation Problem for a $k$-level tree instance is at most $2 - \frac{1}{2^{k-1}}$. For 2- and 3-level trees, these ratios are $\frac32$ and $\frac74$ respectively. Our proofs are constructive and yield polynomial-time approximation algorithms with matching guarantees. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.00148v1-abstract-full').style.display = 'none'; document.getElementById('2111.00148v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.01079">arXiv:2106.01079</a> <span> [<a href="https://arxiv.org/pdf/2106.01079">pdf</a>, <a href="https://arxiv.org/format/2106.01079">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Using Predicted Weights for Ad Delivery </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Lavastida%2C+T">Thomas Lavastida</a>, <a href="/search/cs?searchtype=author&query=Moseley%2C+B">Benjamin Moseley</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Xu%2C+C">Chenyang Xu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2106.01079v1-abstract-short" style="display: inline;"> We study the performance of a proportional weights algorithm for online capacitated bipartite matching modeling the delivery of impression ads. The algorithm uses predictions on the advertiser nodes to match arriving impression nodes fractionally in proportion to the weights of its neighbors. This paper gives a thorough empirical study of the performance of the algorithm on a data-set of ad impres… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.01079v1-abstract-full').style.display = 'inline'; document.getElementById('2106.01079v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.01079v1-abstract-full" style="display: none;"> We study the performance of a proportional weights algorithm for online capacitated bipartite matching modeling the delivery of impression ads. The algorithm uses predictions on the advertiser nodes to match arriving impression nodes fractionally in proportion to the weights of its neighbors. This paper gives a thorough empirical study of the performance of the algorithm on a data-set of ad impressions from Yahoo! and shows its superior performance compared to natural baselines such as a greedy water-filling algorithm and the ranking algorithm. The proportional weights algorithm has recently received interest in the theoretical literature where it was shown to have strong guarantees beyond the worst-case model of algorithms augmented with predictions. We extend these results to the case where the advertisers' capacities are no longer stationary over time. Additionally, we show the algorithm has near optimal performance in the random-order arrival model when the number of impressions and the optimal matching are sufficiently large. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.01079v1-abstract-full').style.display = 'none'; document.getElementById('2106.01079v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 10 figures. To appear in ACDA 2021</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2104.06210">arXiv:2104.06210</a> <span> [<a href="https://arxiv.org/pdf/2104.06210">pdf</a>, <a href="https://arxiv.org/ps/2104.06210">ps</a>, <a href="https://arxiv.org/format/2104.06210">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Performance">cs.PF</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> A simple proof of the Moore-Hodgson Algorithm for minimizing the number of late jobs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Cheriyan%2C+J">Joseph Cheriyan</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Skutella%2C+M">Martin Skutella</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2104.06210v1-abstract-short" style="display: inline;"> The Moore-Hodgson Algorithm minimizes the number of late jobs on a single machine. That is, it finds an optimal schedule for the classical problem $1~|\;|~\sum{U_j}$. Several proofs of the correctness of this algorithm have been published. We present a new short proof. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2104.06210v1-abstract-full" style="display: none;"> The Moore-Hodgson Algorithm minimizes the number of late jobs on a single machine. That is, it finds an optimal schedule for the classical problem $1~|\;|~\sum{U_j}$. Several proofs of the correctness of this algorithm have been published. We present a new short proof. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.06210v1-abstract-full').style.display = 'none'; document.getElementById('2104.06210v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 April, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">3 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 90B35; 68W40 <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> F.2.2 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.08155">arXiv:2103.08155</a> <span> [<a href="https://arxiv.org/pdf/2103.08155">pdf</a>, <a href="https://arxiv.org/format/2103.08155">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> S$^*$: A Heuristic Information-Based Approximation Framework for Multi-Goal Path Finding </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Chour%2C+K">Kenny Chour</a>, <a href="/search/cs?searchtype=author&query=Rathinam%2C+S">Sivakumar Rathinam</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">Ramamoorthi Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2103.08155v2-abstract-short" style="display: inline;"> We combine ideas from uni-directional and bi-directional heuristic search, and approximation algorithms for the Traveling Salesman Problem, to develop a novel framework for a Multi-Goal Path Finding (MGPF) problem that provides a 2-approximation guarantee. MGPF aims to find a least-cost path from an origin to a destination such that each node in a given set of goals is visited at least once along… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.08155v2-abstract-full').style.display = 'inline'; document.getElementById('2103.08155v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.08155v2-abstract-full" style="display: none;"> We combine ideas from uni-directional and bi-directional heuristic search, and approximation algorithms for the Traveling Salesman Problem, to develop a novel framework for a Multi-Goal Path Finding (MGPF) problem that provides a 2-approximation guarantee. MGPF aims to find a least-cost path from an origin to a destination such that each node in a given set of goals is visited at least once along the path. We present numerical results to illustrate the advantages of our framework over conventional alternates in terms of the number of expanded nodes and run time. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.08155v2-abstract-full').style.display = 'none'; document.getElementById('2103.08155v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">In Proceedings of the 31st International Conference on Automated Planning and Scheduling (ICAPS 2021)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2011.11743">arXiv:2011.11743</a> <span> [<a href="https://arxiv.org/pdf/2011.11743">pdf</a>, <a href="https://arxiv.org/format/2011.11743">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Lavastida%2C+T">Thomas Lavastida</a>, <a href="/search/cs?searchtype=author&query=Moseley%2C+B">Benjamin Moseley</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Xu%2C+C">Chenyang Xu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2011.11743v2-abstract-short" style="display: inline;"> We propose a new model for augmenting algorithms with predictions by requiring that they are formally learnable and instance robust. Learnability ensures that predictions can be efficiently constructed from a reasonable amount of past data. Instance robustness ensures that the prediction is robust to modest changes in the problem input, where the measure of the change may be problem specific. Inst… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.11743v2-abstract-full').style.display = 'inline'; document.getElementById('2011.11743v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2011.11743v2-abstract-full" style="display: none;"> We propose a new model for augmenting algorithms with predictions by requiring that they are formally learnable and instance robust. Learnability ensures that predictions can be efficiently constructed from a reasonable amount of past data. Instance robustness ensures that the prediction is robust to modest changes in the problem input, where the measure of the change may be problem specific. Instance robustness insists on a smooth degradation in performance as a function of the change. Ideally, the performance is never worse than worst-case bounds. This also allows predictions to be objectively compared. We design online algorithms with predictions for a network flow allocation problem and restricted assignment makespan minimization. For both problems, two key properties are established: high quality predictions can be learned from a small sample of prior instances and these predictions are robust to errors that smoothly degrade as the underlying problem instance changes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.11743v2-abstract-full').style.display = 'none'; document.getElementById('2011.11743v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">To appear in ESA 2021</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2011.06108">arXiv:2011.06108</a> <span> [<a href="https://arxiv.org/pdf/2011.06108">pdf</a>, <a href="https://arxiv.org/ps/2011.06108">ps</a>, <a href="https://arxiv.org/format/2011.06108">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> An Optimal Rounding for Half-Integral Weighted Minimum Strongly Connected Spanning Subgraph </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Hershkowitz%2C+D+E">D Ellis Hershkowitz</a>, <a href="/search/cs?searchtype=author&query=Kehne%2C+G">Gregory Kehne</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2011.06108v1-abstract-short" style="display: inline;"> In the weighted minimum strongly connected spanning subgraph (WMSCSS) problem we must purchase a minimum-cost strongly connected spanning subgraph of a digraph. We show that half-integral linear program (LP) solutions for WMSCSS can be efficiently rounded to integral solutions at a multiplicative $1.5$ cost. This rounding matches a known $1.5$ integrality gap lower bound for a half-integral instan… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.06108v1-abstract-full').style.display = 'inline'; document.getElementById('2011.06108v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2011.06108v1-abstract-full" style="display: none;"> In the weighted minimum strongly connected spanning subgraph (WMSCSS) problem we must purchase a minimum-cost strongly connected spanning subgraph of a digraph. We show that half-integral linear program (LP) solutions for WMSCSS can be efficiently rounded to integral solutions at a multiplicative $1.5$ cost. This rounding matches a known $1.5$ integrality gap lower bound for a half-integral instance. More generally, we show that LP solutions whose non-zero entries are at least a value $f > 0$ can be rounded at a multiplicative cost of $2 - f$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.06108v1-abstract-full').style.display = 'none'; document.getElementById('2011.06108v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2020. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1911.11229">arXiv:1911.11229</a> <span> [<a href="https://arxiv.org/pdf/1911.11229">pdf</a>, <a href="https://arxiv.org/format/1911.11229">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Downgrading to Minimize Connectivity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Aissi%2C+H">Hassene Aissi</a>, <a href="/search/cs?searchtype=author&query=Chen%2C+D+Q">Da Qi Chen</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1911.11229v1-abstract-short" style="display: inline;"> We study the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We show hardness of obtaining strictly unicriterion approximations for this basic vertex interdiction problem. We also introduce and study a general downgrading variant of the interdiction problem where the capacity of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.11229v1-abstract-full').style.display = 'inline'; document.getElementById('1911.11229v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1911.11229v1-abstract-full" style="display: none;"> We study the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We show hardness of obtaining strictly unicriterion approximations for this basic vertex interdiction problem. We also introduce and study a general downgrading variant of the interdiction problem where the capacity of an arc is a function of the subset of its endpoints that are downgraded, and the goal is to minimize the downgraded capacity of a minimum source-sink cut subject to a node downgrading budget. This models the case when both ends of an arc must be downgraded to remove it, for example. For this generalization, we provide a bicriteria $(4,4)$-approximation that downgrades nodes with total weight at most 4 times the budget and provides a solution where the downgraded connectivity from the source to the sink is at most 4 times that in an optimal solution. WE accomplish this with an LP relaxation and round using a ball-growing algorithm based on the LP values. We further generalize the downgrading problem to one where each vertex can be downgraded to one of $k$ levels, and the arc capacities are functions of the pairs of levels to which its ends are downgraded. We generalize our LP rounding to get $(4k,4k)$-approximation for this case. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.11229v1-abstract-full').style.display = 'none'; document.getElementById('1911.11229v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2019. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1906.04066">arXiv:1906.04066</a> <span> [<a href="https://arxiv.org/pdf/1906.04066">pdf</a>, <a href="https://arxiv.org/format/1906.04066">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">stat.ML</span> </div> </div> <p class="title is-5 mathjax"> Stretching the Effectiveness of MLE from Accuracy to Bias for Pairwise Comparisons </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Wang%2C+J">Jingyan Wang</a>, <a href="/search/cs?searchtype=author&query=Shah%2C+N+B">Nihar B. Shah</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1906.04066v1-abstract-short" style="display: inline;"> A number of applications (e.g., AI bot tournaments, sports, peer grading, crowdsourcing) use pairwise comparison data and the Bradley-Terry-Luce (BTL) model to evaluate a given collection of items (e.g., bots, teams, students, search results). Past work has shown that under the BTL model, the widely-used maximum-likelihood estimator (MLE) is minimax-optimal in estimating the item parameters, in te… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.04066v1-abstract-full').style.display = 'inline'; document.getElementById('1906.04066v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1906.04066v1-abstract-full" style="display: none;"> A number of applications (e.g., AI bot tournaments, sports, peer grading, crowdsourcing) use pairwise comparison data and the Bradley-Terry-Luce (BTL) model to evaluate a given collection of items (e.g., bots, teams, students, search results). Past work has shown that under the BTL model, the widely-used maximum-likelihood estimator (MLE) is minimax-optimal in estimating the item parameters, in terms of the mean squared error. However, another important desideratum for designing estimators is fairness. In this work, we consider fairness modeled by the notion of bias in statistics. We show that the MLE incurs a suboptimal rate in terms of bias. We then propose a simple modification to the MLE, which "stretches" the bounding box of the maximum-likelihood optimizer by a small constant factor from the underlying ground truth domain. We show that this simple modification leads to an improved rate in bias, while maintaining minimax-optimality in the mean squared error. In this manner, our proposed class of estimators provably improves fairness represented by bias without loss in accuracy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.04066v1-abstract-full').style.display = 'none'; document.getElementById('1906.04066v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 June, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2019. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1905.00148">arXiv:1905.00148</a> <span> [<a href="https://arxiv.org/pdf/1905.00148">pdf</a>, <a href="https://arxiv.org/ps/1905.00148">ps</a>, <a href="https://arxiv.org/format/1905.00148">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Inventory Routing Problem with Facility Location </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Jiao%2C+Y">Yang Jiao</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1905.00148v1-abstract-short" style="display: inline;"> We study problems that integrate depot location decisions along with the inventory routing problem of serving clients from these depots over time balancing the costs of routing vehicles from the depots with the holding costs of demand delivered before they are due. Since the inventory routing problem is already complex, we study the version that assumes that the daily vehicle routes are direct con… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.00148v1-abstract-full').style.display = 'inline'; document.getElementById('1905.00148v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1905.00148v1-abstract-full" style="display: none;"> We study problems that integrate depot location decisions along with the inventory routing problem of serving clients from these depots over time balancing the costs of routing vehicles from the depots with the holding costs of demand delivered before they are due. Since the inventory routing problem is already complex, we study the version that assumes that the daily vehicle routes are direct connections from the depot thus forming stars as solutions, and call this problem the Star Inventory Routing Problem with Facility Location (SIRPFL). As a stepping stone to solving SIRPFL, we first study the Inventory Access Problem (IAP), which is the single depot, single client special case of IRP. The Uncapacitated IAP is known to have a polynomial time dynamic program. We provide an NP-hardness reduction for Capacitated IAP where each demand cannot be split among different trips. We give a $3$-approximation for the case when demands can be split and a $6$-approximation for the unsplittable case. For Uncapacitated SIRPFL, we provide a $12$-approximation by rounding an LP relaxation. Combining the ideas from Capacitated IAP and Uncapacitated SIRPFL, we obtain a $24$-approximation for Capacitated Splittable SIRPFL and a $48$-approximation for the most general version, the Capacitated Unsplittable SIRPFL. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.00148v1-abstract-full').style.display = 'none'; document.getElementById('1905.00148v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages, preprint, full version of paper to appear in WADS 2019</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.03030">arXiv:1812.03030</a> <span> [<a href="https://arxiv.org/pdf/1812.03030">pdf</a>, <a href="https://arxiv.org/format/1812.03030">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Retrieval">cs.IR</span> </div> </div> <p class="title is-5 mathjax"> A new system-wide diversity measure for recommendations with efficient algorithms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Antikacioglu%2C+A">Arda Antikacioglu</a>, <a href="/search/cs?searchtype=author&query=Bajpai%2C+T">Tanvi Bajpai</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1812.03030v2-abstract-short" style="display: inline;"> Recommender systems often operate on item catalogs clustered by genres, and user bases that have natural clusterings into user types by demographic or psychographic attributes. Prior work on system-wide diversity has mainly focused on defining intent-aware metrics among such categories and maximizing relevance of the resulting recommendations, but has not combined the notions of diversity from the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.03030v2-abstract-full').style.display = 'inline'; document.getElementById('1812.03030v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.03030v2-abstract-full" style="display: none;"> Recommender systems often operate on item catalogs clustered by genres, and user bases that have natural clusterings into user types by demographic or psychographic attributes. Prior work on system-wide diversity has mainly focused on defining intent-aware metrics among such categories and maximizing relevance of the resulting recommendations, but has not combined the notions of diversity from the two point of views of items and users. In this work, (1) we introduce two new system-wide diversity metrics to simultaneously address the problems of diversifying the categories of items that each user sees, diversifying the types of users that each item is shown, and maintaining high recommendation quality. We model this as a subgraph selection problem on the bipartite graph of candidate recommendations between users and items. (2) In the case of disjoint item categories and user types, we show that the resulting problems can be solved exactly in polynomial time, by a reduction to a minimum cost flow problem. (3) In the case of non-disjoint categories and user types, we prove NP-completeness of the objective and present efficient approximation algorithms using the submodularity of the objective. (4) Finally, we validate the effectiveness of our algorithms on the MovieLens-1m and Netflix datasets, and show that algorithms designed for our objective also perform well on sales diversity metrics, and even some intent-aware diversity metrics. Our experimental results justify the validity of our new composite diversity metrics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.03030v2-abstract-full').style.display = 'none'; document.getElementById('1812.03030v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 November, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 05C85; 68R10; 68W25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1811.11635">arXiv:1811.11635</a> <span> [<a href="https://arxiv.org/pdf/1811.11635">pdf</a>, <a href="https://arxiv.org/ps/1811.11635">ps</a>, <a href="https://arxiv.org/format/1811.11635">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Prepare for the Expected Worst: Algorithms for Reconfigurable Resources Under Uncertainty </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Hershkowitz%2C+D+E">D Ellis Hershkowitz</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Singla%2C+S">Sahil Singla</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1811.11635v2-abstract-short" style="display: inline;"> In this paper we study how to optimally balance cheap inflexible resources with more expensive, reconfigurable resources despite uncertainty in the input problem. Specifically, we introduce the MinEMax model to study "build versus rent" problems. In our model different scenarios appear independently. Before knowing which scenarios appear, we may build rigid resources that cannot be changed for dif… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1811.11635v2-abstract-full').style.display = 'inline'; document.getElementById('1811.11635v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1811.11635v2-abstract-full" style="display: none;"> In this paper we study how to optimally balance cheap inflexible resources with more expensive, reconfigurable resources despite uncertainty in the input problem. Specifically, we introduce the MinEMax model to study "build versus rent" problems. In our model different scenarios appear independently. Before knowing which scenarios appear, we may build rigid resources that cannot be changed for different scenarios. Once we know which scenarios appear, we are allowed to rent reconfigurable but expensive resources to use across scenarios. Although computing the objective in our model might seem to require enumerating exponentially-many possibilities, we show it is well-estimated by a surrogate objective which is representable by a polynomial-size LP. In this surrogate objective we pay for each scenario only to the extent that it exceeds a certain threshold. Using this objective we design algorithms that approximately-optimally balance inflexible and reconfigurable resources for several NP-hard covering problems. For example, we study minimum spanning and Steiner trees, minimum cuts and facility location variants. Up to constants our approximation guarantees match those of previous algorithms for the previously-studied demand-robust and stochastic two-stage models. Lastly, we demonstrate that our problem is sufficiently general to smoothly interpolate between previous demand-robust and stochastic two-stage problems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1811.11635v2-abstract-full').style.display = 'none'; document.getElementById('1811.11635v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 November, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Corrected several typos</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1712.05218">arXiv:1712.05218</a> <span> [<a href="https://arxiv.org/pdf/1712.05218">pdf</a>, <a href="https://arxiv.org/format/1712.05218">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Approximation Algorithms for Replenishment Problems with Fixed Turnover Times </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Bosman%2C+T">Thomas Bosman</a>, <a href="/search/cs?searchtype=author&query=van+Ee%2C+M">Martijn van Ee</a>, <a href="/search/cs?searchtype=author&query=Jiao%2C+Y">Yang Jiao</a>, <a href="/search/cs?searchtype=author&query=Marchetti-Spaccamela%2C+A">Alberto Marchetti-Spaccamela</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Stougie%2C+L">Leen Stougie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1712.05218v1-abstract-short" style="display: inline;"> We introduce and study a class of optimization problems we coin replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Nodes with capacity for storing a certain commodity are located at various places; at each node the commodity depletes within a certain time, the turnover time, which is constant but can vary between locations.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.05218v1-abstract-full').style.display = 'inline'; document.getElementById('1712.05218v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1712.05218v1-abstract-full" style="display: none;"> We introduce and study a class of optimization problems we coin replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Nodes with capacity for storing a certain commodity are located at various places; at each node the commodity depletes within a certain time, the turnover time, which is constant but can vary between locations. Nodes should never run empty, and to prevent this we may schedule nodes for replenishment every day. The natural feature that makes this problem interesting is that we may schedule a replenishment (well) before a node becomes empty, but then the next replenishment will be due earlier also. This added workload needs to be balanced against the cost of routing vehicles to do the replenishments. In this paper, we focus on the aspect of minimizing routing costs. However, the framework of recurring tasks, in which the next job of a task must be done within a fixed amount of time after the previous one is much more general and gives an adequate model for many practical situations. Note that our problem has an infinite time horizon. However, it can be fully characterized by a compact input, containing only the location of each store and a turnover time. This makes determining its computational complexity highly challenging and indeed it remains essentially unresolved. We study the problem for two objectives: min-avg minimizes the average tour length and min-max minimizes the maximum tour length over all days. For min-max we derive a logarithmic factor approximation for the problem on general metrics and a 6-approximation for the problem on trees, for which we have a proof of NP-hardness. For min-avg we present a logarithmic approximation on general metrics, 2-approximation for trees, and a pseudopolynomial time algorithm for the line. Many intriguing problems remain open. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.05218v1-abstract-full').style.display = 'none'; document.getElementById('1712.05218v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 December, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> F.2.2; G.2.2 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1707.05387">arXiv:1707.05387</a> <span> [<a href="https://arxiv.org/pdf/1707.05387">pdf</a>, <a href="https://arxiv.org/format/1707.05387">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Shorter tours and longer detours: Uniform covers and a bit beyond </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Haddadan%2C+A">Arash Haddadan</a>, <a href="/search/cs?searchtype=author&query=Newman%2C+A">Alantha Newman</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1707.05387v4-abstract-short" style="display: inline;"> Motivated by the well known four-thirds conjecture for the traveling salesman problem (TSP), we study the problem of {\em uniform covers}. A graph $G=(V,E)$ has an $伪$-uniform cover for TSP (2EC, respectively) if the everywhere $伪$ vector (i.e. $\{伪\}^{E}$) dominates a convex combination of incidence vectors of tours (2-edge-connected spanning multigraphs, respectively). The polyhedral analysis of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.05387v4-abstract-full').style.display = 'inline'; document.getElementById('1707.05387v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1707.05387v4-abstract-full" style="display: none;"> Motivated by the well known four-thirds conjecture for the traveling salesman problem (TSP), we study the problem of {\em uniform covers}. A graph $G=(V,E)$ has an $伪$-uniform cover for TSP (2EC, respectively) if the everywhere $伪$ vector (i.e. $\{伪\}^{E}$) dominates a convex combination of incidence vectors of tours (2-edge-connected spanning multigraphs, respectively). The polyhedral analysis of Christofides' algorithm directly implies that a 3-edge-connected, cubic graph has a 1-uniform cover for TSP. Seb艖 asked if such graphs have $(1-蔚)$-uniform covers for TSP for some $蔚> 0$. Indeed, the four-thirds conjecture implies that such graphs have 8/9-uniform covers. We show that these graphs have 18/19-uniform covers for TSP. We also study uniform covers for 2EC and show that the everywhere 15/17 vector can be efficiently written as a convex combination of 2-edge-connected spanning multigraphs. For a weighted, 3-edge-connected, cubic graph, our results show that if the everywhere 2/3 vector is an optimal solution for the subtour linear programming relaxation, then a tour with weight at most 27/19 times that of an optimal tour can be found efficiently. Node-weighted, 3-edge-connected, cubic graphs fall into this category. In this special case, we can apply our tools to obtain an even better approximation guarantee. To extend our approach to input graphs that are 2-edge-connected, we present a procedure to decompose an optimal solution for the subtour relaxation for TSP into spanning, connected multigraphs that cover each 2-edge cut an even number of times. Using this decomposition, we obtain a 17/12-approximation algorithm for minimum weight 2-edge-connected spanning subgraphs on subcubic, node-weighted graphs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.05387v4-abstract-full').style.display = 'none'; document.getElementById('1707.05387v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2017. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1707.05240">arXiv:1707.05240</a> <span> [<a href="https://arxiv.org/pdf/1707.05240">pdf</a>, <a href="https://arxiv.org/ps/1707.05240">ps</a>, <a href="https://arxiv.org/format/1707.05240">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Coloring Down: $3/2$-approximation for special cases of the weighted tree augmentation problem </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Iglesias%2C+J">Jennifer Iglesias</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1707.05240v1-abstract-short" style="display: inline;"> In this paper, we investigate the weighted tree augmentation problem (TAP), where the goal is to augment a tree with a minimum cost set of edges such that the graph becomes two edge connected. First we show that in weighted TAP, we can restrict our attention to trees which are binary and where all the non-tree edges go between two leaves of the tree. We then give two different top-down coloring al… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.05240v1-abstract-full').style.display = 'inline'; document.getElementById('1707.05240v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1707.05240v1-abstract-full" style="display: none;"> In this paper, we investigate the weighted tree augmentation problem (TAP), where the goal is to augment a tree with a minimum cost set of edges such that the graph becomes two edge connected. First we show that in weighted TAP, we can restrict our attention to trees which are binary and where all the non-tree edges go between two leaves of the tree. We then give two different top-down coloring algorithms. Both algorithms differ from known techniques for a 3/2-approximation in unweighted TAP and current attempts to reach a 3/2-approximation for weighted TAP. The first algorithm we describe always gives a 2-approximation for any feasible fractional solution to the natural edge cover LP. When the fractional solution is such that all the edges with non-zero weight are at least $伪$, then this algorithm achieves a $2/(1+伪)$-approximation. We propose a new conjecture on extreme points of LP relaxations for the problem, which if true, will lead to a constructive proof of an integrality gap of at most 3/2 for weighted TAP. In the second algorithm, we introduce simple valid constraints to the edge cover LP. In this algorithm, we focus on deficient edges, edges covered to an extent less than 4/3 in the fractional solution. We show that for fractional feasible solutions, deficient edges occur in node-disjoint paths in the tree. When the number of such paths is at most two, we give a top-down coloring algorithm which decomposes 3/2 times the fractional solution into a convex combination of integer solutions. We believe our algorithms will be useful in eventually resolving the integrality gap of linear programming formulations for TAP. We also investigate a variant of TAP where each edge in the solution must be covered by a cycle of length three. We give a $螛(\log n)$-approximation algorithm for this problem in the weighted case and a 4-approximation in the unweighted case. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.05240v1-abstract-full').style.display = 'none'; document.getElementById('1707.05240v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> F.2.2; G.2.2 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1707.01487">arXiv:1707.01487</a> <span> [<a href="https://arxiv.org/pdf/1707.01487">pdf</a>, <a href="https://arxiv.org/format/1707.01487">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Single-sink Fractionally Subadditive Network Design </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Guruganesh%2C+G">Guru Guruganesh</a>, <a href="/search/cs?searchtype=author&query=Iglesias%2C+J">Jennifer Iglesias</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Sanit%C3%A0%2C+L">Laura Sanit脿</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1707.01487v2-abstract-short" style="display: inline;"> We study a generalization of the Steiner tree problem, where we are given a weighted network $G$ together with a collection of $k$ subsets of its vertices and a root $r$. We wish to construct a minimum cost network such that the network supports one unit of flow to the root from every node in a subset simultaneously. The network constructed does not need to support flows from all the subsets simul… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.01487v2-abstract-full').style.display = 'inline'; document.getElementById('1707.01487v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1707.01487v2-abstract-full" style="display: none;"> We study a generalization of the Steiner tree problem, where we are given a weighted network $G$ together with a collection of $k$ subsets of its vertices and a root $r$. We wish to construct a minimum cost network such that the network supports one unit of flow to the root from every node in a subset simultaneously. The network constructed does not need to support flows from all the subsets simultaneously. We settle an open question regarding the complexity of this problem for $k=2$, and give a $\frac{3}{2}$-approximation algorithm that improves over a (trivial) known 2-approximation. Furthermore, we prove some structural results that prevent many well-known techniques from doing better than the known $O(\log n)$-approximation. Despite these obstacles, we conjecture that this problem should have an $O(1)$-approximation. We also give an approximation result for a variant of the problem where the solution is required to be a path. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.01487v2-abstract-full').style.display = 'none'; document.getElementById('1707.01487v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> F.2.2; G.2.2 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1706.06565">arXiv:1706.06565</a> <span> [<a href="https://arxiv.org/pdf/1706.06565">pdf</a>, <a href="https://arxiv.org/format/1706.06565">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> On the Integrality Gap of the Prize-Collecting Steiner Forest LP </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=K%C3%B6nemann%2C+J">Jochen K枚nemann</a>, <a href="/search/cs?searchtype=author&query=Olver%2C+N">Neil Olver</a>, <a href="/search/cs?searchtype=author&query=Pashkovich%2C+K">Kanstantsin Pashkovich</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Swamy%2C+C">Chaitanya Swamy</a>, <a href="/search/cs?searchtype=author&query=Vygen%2C+J">Jens Vygen</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1706.06565v1-abstract-short" style="display: inline;"> In the prize-collecting Steiner forest (PCSF) problem, we are given an undirected graph $G=(V,E)$, edge costs $\{c_e\geq 0\}_{e\in E}$, terminal pairs $\{(s_i,t_i)\}_{i=1}^k$, and penalties $\{蟺_i\}_{i=1}^k$ for each terminal pair; the goal is to find a forest $F$ to minimize $c(F)+\sum_{i: (s_i,t_i)\text{ not connected in }F}蟺_i$. The Steiner forest problem can be viewed as the special case where… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1706.06565v1-abstract-full').style.display = 'inline'; document.getElementById('1706.06565v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1706.06565v1-abstract-full" style="display: none;"> In the prize-collecting Steiner forest (PCSF) problem, we are given an undirected graph $G=(V,E)$, edge costs $\{c_e\geq 0\}_{e\in E}$, terminal pairs $\{(s_i,t_i)\}_{i=1}^k$, and penalties $\{蟺_i\}_{i=1}^k$ for each terminal pair; the goal is to find a forest $F$ to minimize $c(F)+\sum_{i: (s_i,t_i)\text{ not connected in }F}蟺_i$. The Steiner forest problem can be viewed as the special case where $蟺_i=\infty$ for all $i$. It was widely believed that the integrality gap of the natural (and well-studied) linear-programming (LP) relaxation for PCSF is at most 2. We dispel this belief by showing that the integrality gap of this LP is at least $9/4$. This holds even for planar graphs. We also show that using this LP, one cannot devise a Lagrangian-multiplier-preserving (LMP) algorithm with approximation guarantee better than $4$. Our results thus show a separation between the integrality gaps of the LP-relaxations for prize-collecting and non-prize-collecting (i.e., standard) Steiner forest, as well as the approximation ratios achievable relative to the optimal LP solution by LMP- and non-LMP- approximation algorithms for PCSF. For the special case of prize-collecting Steiner tree (PCST), we prove that the natural LP relaxation admits basic feasible solutions with all coordinates of value at most $1/3$ and all edge variables positive. Thus, we rule out the possibility of approximating PCST with guarantee better than $3$ using a direct iterative rounding method. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1706.06565v1-abstract-full').style.display = 'none'; document.getElementById('1706.06565v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 June, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2017. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1702.05446">arXiv:1702.05446</a> <span> [<a href="https://arxiv.org/pdf/1702.05446">pdf</a>, <a href="https://arxiv.org/format/1702.05446">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Retrieval">cs.IR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Network Flow Based Post Processing for Sales Diversity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Antikacioglu%2C+A">Arda Antikacioglu</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1702.05446v1-abstract-short" style="display: inline;"> Collaborative filtering is a broad and powerful framework for building recommendation systems that has seen widespread adoption. Over the past decade, the propensity of such systems for favoring popular products and thus creating echo chambers have been observed. This has given rise to an active area of research that seeks to diversify recommendations generated by such algorithms. We address the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1702.05446v1-abstract-full').style.display = 'inline'; document.getElementById('1702.05446v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1702.05446v1-abstract-full" style="display: none;"> Collaborative filtering is a broad and powerful framework for building recommendation systems that has seen widespread adoption. Over the past decade, the propensity of such systems for favoring popular products and thus creating echo chambers have been observed. This has given rise to an active area of research that seeks to diversify recommendations generated by such algorithms. We address the problem of increasing diversity in recommendation systems that are based on collaborative filtering that use past ratings to predicting a rating quality for potential recommendations. Following our earlier work, we formulate recommendation system design as a subgraph selection problem from a candidate super-graph of potential recommendations where both diversity and rating quality are explicitly optimized: (1) On the modeling side, we define a new flexible notion of diversity that allows a system designer to prescribe the number of recommendations each item should receive, and smoothly penalizes deviations from this distribution. (2) On the algorithmic side, we show that minimum-cost network flow methods yield fast algorithms in theory and practice for designing recommendation subgraphs that optimize this notion of diversity. (3) On the empirical side, we show the effectiveness of our new model and method to increase diversity while maintaining high rating quality in standard rating data sets from Netflix and MovieLens. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1702.05446v1-abstract-full').style.display = 'none'; document.getElementById('1702.05446v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 February, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2017. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1612.04794">arXiv:1612.04794</a> <span> [<a href="https://arxiv.org/pdf/1612.04794">pdf</a>, <a href="https://arxiv.org/format/1612.04794">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Algorithms for Automatic Ranking of Participants and Tasks in an Anonymized Contest </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Jiao%2C+Y">Yang Jiao</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Gatterbauer%2C+W">Wolfgang Gatterbauer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1612.04794v2-abstract-short" style="display: inline;"> We introduce a new set of problems based on the Chain Editing problem. In our version of Chain Editing, we are given a set of anonymous participants and a set of undisclosed tasks that every participant attempts. For each participant-task pair, we know whether the participant has succeeded at the task or not. We assume that participants vary in their ability to solve tasks, and that tasks vary in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1612.04794v2-abstract-full').style.display = 'inline'; document.getElementById('1612.04794v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1612.04794v2-abstract-full" style="display: none;"> We introduce a new set of problems based on the Chain Editing problem. In our version of Chain Editing, we are given a set of anonymous participants and a set of undisclosed tasks that every participant attempts. For each participant-task pair, we know whether the participant has succeeded at the task or not. We assume that participants vary in their ability to solve tasks, and that tasks vary in their difficulty to be solved. In an ideal world, stronger participants should succeed at a superset of tasks that weaker participants succeed at. Similarly, easier tasks should be completed successfully by a superset of participants who succeed at harder tasks. In reality, it can happen that a stronger participant fails at a task that a weaker participants succeeds at. Our goal is to find a perfect nesting of the participant-task relations by flipping a minimum number of participant-task relations, implying such a "nearest perfect ordering" to be the one that is closest to the truth of participant strengths and task difficulties. Many variants of the problem are known to be NP-hard. We propose six natural $k$-near versions of the Chain Editing problem and classify their complexity. The input to a $k$-near Chain Editing problem includes an initial ordering of the participants (or tasks) that we are required to respect by moving each participant (or task) at most $k$ positions from the initial ordering. We obtain surprising results on the complexity of the six $k$-near problems: Five of the problems are polynomial-time solvable using dynamic programming, but one of them is NP-hard. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1612.04794v2-abstract-full').style.display = 'none'; document.getElementById('1612.04794v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 December, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 December, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">21 pages, 5 figures, preprint, full version of paper to appear in WALCOM 2017</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1612.01492">arXiv:1612.01492</a> <span> [<a href="https://arxiv.org/pdf/1612.01492">pdf</a>, <a href="https://arxiv.org/ps/1612.01492">ps</a>, <a href="https://arxiv.org/format/1612.01492">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Plane Gossip: Approximating rumor spread in planar graphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Iglesias%2C+J">Jennifer Iglesias</a>, <a href="/search/cs?searchtype=author&query=Rajaraman%2C+R">Rajmohan Rajaraman</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R Ravi</a>, <a href="/search/cs?searchtype=author&query=Sundaram%2C+R">Ravi Sundaram</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1612.01492v2-abstract-short" style="display: inline;"> We study the design of schedules for multi-commodity multicast; we are given an undirected graph $G$ and a collection of source destination pairs, and the goal is to schedule a minimum-length sequence of matchings that connects every source with its respective destination. Multi-commodity multicast models a classic information dissemination problem in networks where the primary communication const… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1612.01492v2-abstract-full').style.display = 'inline'; document.getElementById('1612.01492v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1612.01492v2-abstract-full" style="display: none;"> We study the design of schedules for multi-commodity multicast; we are given an undirected graph $G$ and a collection of source destination pairs, and the goal is to schedule a minimum-length sequence of matchings that connects every source with its respective destination. Multi-commodity multicast models a classic information dissemination problem in networks where the primary communication constraint is the number of connections that a node can make, not link bandwidth. Multi-commodity multicast is closely related to the problem of finding a subgraph, $H$, of optimal poise, where the poise is defined as the sum of the maximum degree of $H$ and the maximum distance between any source-destination pair in $H$. We first show that the minimum poise subgraph for single-commodity multicast can be approximated to within a factor of $O(\log k)$ with respect to the value of a natural LP relaxation in an instance with $k$ terminals. This is the first upper bound on the integrality gap of the natural LP. Using this poise result and shortest-path separators in planar graphs, we obtain a $O(\log^3 k\log n/(\log\log n))$-approximation for multi-commodity multicast for planar graphs. We also study the minimum-time radio gossip problem in planar graphs where a message from each node must be transmitted to all other nodes under a model where nodes can broadcast to all neighbors in a single step but only nodes with a single broadcasting neighbor get a message. We give an $O(\log^2 n)$-approximation for radio gossip in planar graphs breaking previous barriers. This is the first bound for radio gossip that does not rely on the maximum degree of the graph. Finally, we show that our techniques for planar graphs extend to graphs with excluded minors. We establish polylogarithmic-approximation algorithms for both multi-commodity multicast and radio gossip problems in minor-free graphs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1612.01492v2-abstract-full').style.display = 'none'; document.getElementById('1612.01492v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 December, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> F.2.2; G.2.2 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.00052">arXiv:1611.00052</a> <span> [<a href="https://arxiv.org/pdf/1611.00052">pdf</a>, <a href="https://arxiv.org/format/1611.00052">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> LAST but not Least: Online Spanners for Buy-at-Bulk </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gupta%2C+A">Anupam Gupta</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Talwar%2C+K">Kunal Talwar</a>, <a href="/search/cs?searchtype=author&query=Umboh%2C+S+W">Seeun William Umboh</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1611.00052v1-abstract-short" style="display: inline;"> The online (uniform) buy-at-bulk network design problem asks us to design a network, where the edge-costs exhibit economy-of-scale. Previous approaches to this problem used tree- embeddings, giving us randomized algorithms. Moreover, the optimal results with a logarithmic competitive ratio requires the metric on which the network is being built to be known up-front; the competitive ratios then dep… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.00052v1-abstract-full').style.display = 'inline'; document.getElementById('1611.00052v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.00052v1-abstract-full" style="display: none;"> The online (uniform) buy-at-bulk network design problem asks us to design a network, where the edge-costs exhibit economy-of-scale. Previous approaches to this problem used tree- embeddings, giving us randomized algorithms. Moreover, the optimal results with a logarithmic competitive ratio requires the metric on which the network is being built to be known up-front; the competitive ratios then depend on the size of this metric (which could be much larger than the number of terminals that arrive). We consider the buy-at-bulk problem in the least restrictive model where the metric is not known in advance, but revealed in parts along with the demand points seeking connectivity arriving online. For the single sink buy-at-bulk problem, we give a deterministic online algorithm with competitive ratio that is logarithmic in k, the number of terminals that have arrived, matching the lower bound known even for the online Steiner tree problem. In the oblivious case when the buy-at-bulk function used to compute the edge-costs of the network is not known in advance (but is the same across all edges), we give a deterministic algorithm with competitive ratio polylogarithmic in k, the number of terminals. At the heart of our algorithms are optimal constructions for online Light Approximate Shortest-path Trees (LASTs) and spanners, and their variants. We give constructions that have optimal trade-offs in terms of cost and stretch. We also define and give constructions for a new notion of LASTs where the set of roots (in addition to the points) expands over time. We expect these techniques will find applications in other online network-design problems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.00052v1-abstract-full').style.display = 'none'; document.getElementById('1611.00052v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1605.07196">arXiv:1605.07196</a> <span> [<a href="https://arxiv.org/pdf/1605.07196">pdf</a>, <a href="https://arxiv.org/format/1605.07196">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Networking and Internet Architecture">cs.NI</span> </div> </div> <p class="title is-5 mathjax"> Balls and Funnels: Energy Efficient Group-to-Group Anycasts </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Iglesias%2C+J">Jennifer Iglesias</a>, <a href="/search/cs?searchtype=author&query=Rajaraman%2C+R">Rajmohan Rajaraman</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Sundaram%2C+R">Ravi Sundaram</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1605.07196v1-abstract-short" style="display: inline;"> We introduce group-to-group anycast (g2g-anycast), a network design problem of substantial practical importance and considerable generality. Given a collection of groups and requirements for directed connectivity from source groups to destination groups, the solution network must contain, for each requirement, an omni-directional down-link broadcast, centered at any node of the source group, calle… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1605.07196v1-abstract-full').style.display = 'inline'; document.getElementById('1605.07196v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1605.07196v1-abstract-full" style="display: none;"> We introduce group-to-group anycast (g2g-anycast), a network design problem of substantial practical importance and considerable generality. Given a collection of groups and requirements for directed connectivity from source groups to destination groups, the solution network must contain, for each requirement, an omni-directional down-link broadcast, centered at any node of the source group, called the ball; the ball must contain some node from the destination group in the requirement and all such destination nodes in the ball must aggregate into a tree directed towards the source, called the funnel-tree. The solution network is a collection of balls along with the funnel-trees they contain. g2g-anycast models DBS (Digital Broadcast Satellite), Cable TV systems and drone swarms. It generalizes several well known network design problems including minimum energy unicast, multicast, broadcast, Steiner-tree, Steiner-forest and Group-Steiner tree. Our main achievement is an $O(\log^4 n)$ approximation, counterbalanced by an $\log^{(2-蔚)}n$ hardness of approximation, for general weights. Given the applicability to wireless communication, we present a scalable and easily implemented $O(\log n)$ approximation algorithm, Cover-and-Grow for fixed-dimensional Euclidean space with path-loss exponent at least 2. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1605.07196v1-abstract-full').style.display = 'none'; document.getElementById('1605.07196v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 May, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2016. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1409.2042">arXiv:1409.2042</a> <span> [<a href="https://arxiv.org/pdf/1409.2042">pdf</a>, <a href="https://arxiv.org/format/1409.2042">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Retrieval">cs.IR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Recommendation Subgraphs for Web Discovery </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Antikacioglu%2C+A">Arda Antikacioglu</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Srihdar%2C+S">Srinath Srihdar</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1409.2042v1-abstract-short" style="display: inline;"> Recommendations are central to the utility of many websites including YouTube, Quora as well as popular e-commerce stores. Such sites typically contain a set of recommendations on every product page that enables visitors to easily navigate the website. Choosing an appropriate set of recommendations at each page is one of the key features of backend engines that have been deployed at several e-comm… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1409.2042v1-abstract-full').style.display = 'inline'; document.getElementById('1409.2042v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1409.2042v1-abstract-full" style="display: none;"> Recommendations are central to the utility of many websites including YouTube, Quora as well as popular e-commerce stores. Such sites typically contain a set of recommendations on every product page that enables visitors to easily navigate the website. Choosing an appropriate set of recommendations at each page is one of the key features of backend engines that have been deployed at several e-commerce sites. Specifically at BloomReach, an engine consisting of several independent components analyzes and optimizes its clients' websites. This paper focuses on the structure optimizer component which improves the website navigation experience that enables the discovery of novel content. We begin by formalizing the concept of recommendations used for discovery. We formulate this as a natural graph optimization problem which in its simplest case, reduces to a bipartite matching problem. In practice, solving these matching problems requires superlinear time and is not scalable. Also, implementing simple algorithms is critical in practice because they are significantly easier to maintain in production. This motivated us to analyze three methods for solving the problem in increasing order of sophistication: a sampling algorithm, a greedy algorithm and a more involved partitioning based algorithm. We first theoretically analyze the performance of these three methods on random graph models characterizing when each method will yield a solution of sufficient quality and the parameter ranges when more sophistication is needed. We complement this by providing an empirical analysis of these algorithms on simulated and real-world production data. Our results confirm that it is not always necessary to implement complicated algorithms in the real-world and that very good practical results can be obtained by using heuristics that are backed by the confidence of concrete theoretical guarantees. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1409.2042v1-abstract-full').style.display = 'none'; document.getElementById('1409.2042v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 September, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2014. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1407.2844">arXiv:1407.2844</a> <span> [<a href="https://arxiv.org/pdf/1407.2844">pdf</a>, <a href="https://arxiv.org/ps/1407.2844">ps</a>, <a href="https://arxiv.org/format/1407.2844">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Graph-TSP from Steiner Cycles </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Iwata%2C+S">Satoru Iwata</a>, <a href="/search/cs?searchtype=author&query=Newman%2C+A">Alantha Newman</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1407.2844v1-abstract-short" style="display: inline;"> We present an approach for the traveling salesman problem with graph metric based on Steiner cycles. A Steiner cycle is a cycle that is required to contain some specified subset of vertices. For a graph $G$, if we can find a spanning tree $T$ and a simple cycle that contains the vertices with odd-degree in $T$, then we show how to combine the classic "double spanning tree" algorithm with Christofi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1407.2844v1-abstract-full').style.display = 'inline'; document.getElementById('1407.2844v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1407.2844v1-abstract-full" style="display: none;"> We present an approach for the traveling salesman problem with graph metric based on Steiner cycles. A Steiner cycle is a cycle that is required to contain some specified subset of vertices. For a graph $G$, if we can find a spanning tree $T$ and a simple cycle that contains the vertices with odd-degree in $T$, then we show how to combine the classic "double spanning tree" algorithm with Christofides' algorithm to obtain a TSP tour of length at most $\frac{4n}{3}$. We use this approach to show that a graph containing a Hamiltonian path has a TSP tour of length at most $4n/3$. Since a Hamiltonian path is a spanning tree with two leaves, this motivates the question of whether or not a graph containing a spanning tree with few leaves has a short TSP tour. The recent techniques of M枚mke and Svensson imply that a graph containing a depth-first-search tree with $k$ leaves has a TSP tour of length $4n/3 + O(k)$. Using our approach, we can show that a $2(k-1)$-vertex connected graph that contains a spanning tree with at most $k$ leaves has a TSP tour of length $4n/3$. We also explore other conditions under which our approach results in a short tour. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1407.2844v1-abstract-full').style.display = 'none'; document.getElementById('1407.2844v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 July, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Proceedings of WG 2014</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1311.3640">arXiv:1311.3640</a> <span> [<a href="https://arxiv.org/pdf/1311.3640">pdf</a>, <a href="https://arxiv.org/ps/1311.3640">ps</a>, <a href="https://arxiv.org/format/1311.3640">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> A 9/7-Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Karp%2C+J">Jeremy Karp</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1311.3640v2-abstract-short" style="display: inline;"> We prove new results for approximating Graphic TSP. Specifically, we provide a polynomial-time \frac{9}{7}-approximation algorithm for cubic bipartite graphs and a (\frac{9}{7}+\frac{1}{21(k-2)})-approximation algorithm for k-regular bipartite graphs, both of which are improved approximation factors compared to previous results. Our approach involves finding a cycle cover with relatively few cycle… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1311.3640v2-abstract-full').style.display = 'inline'; document.getElementById('1311.3640v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1311.3640v2-abstract-full" style="display: none;"> We prove new results for approximating Graphic TSP. Specifically, we provide a polynomial-time \frac{9}{7}-approximation algorithm for cubic bipartite graphs and a (\frac{9}{7}+\frac{1}{21(k-2)})-approximation algorithm for k-regular bipartite graphs, both of which are improved approximation factors compared to previous results. Our approach involves finding a cycle cover with relatively few cycles, which we are able to do by leveraging the fact that all cycles in bipartite graphs are of even length along with our knowledge of the structure of cubic graphs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1311.3640v2-abstract-full').style.display = 'none'; document.getElementById('1311.3640v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 October, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 November, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2013. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1205.1477">arXiv:1205.1477</a> <span> [<a href="https://arxiv.org/pdf/1205.1477">pdf</a>, <a href="https://arxiv.org/ps/1205.1477">ps</a>, <a href="https://arxiv.org/format/1205.1477">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Approximation Algorithms for Online Weighted Rank Function Maximization under Matroid Constraints </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Buchbinder%2C+N">Niv Buchbinder</a>, <a href="/search/cs?searchtype=author&query=Joseph"> Joseph</a>, <a href="/search/cs?searchtype=author&query=Naor"> Naor</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a>, <a href="/search/cs?searchtype=author&query=Singh%2C+M">Mohit Singh</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1205.1477v1-abstract-short" style="display: inline;"> Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent in the matroid over time. At each time, a new weighted rank function of a different matroid (one per time) over the same elements is presented; the algorithm can… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1205.1477v1-abstract-full').style.display = 'inline'; document.getElementById('1205.1477v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1205.1477v1-abstract-full" style="display: none;"> Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent in the matroid over time. At each time, a new weighted rank function of a different matroid (one per time) over the same elements is presented; the algorithm can add a few elements to the incrementally constructed set, and reaps a reward equal to the value of the new weighted rank function on the current set. The goal of the algorithm as it builds this independent set online is to maximize the sum of these (weighted rank) rewards. As in regular online analysis, we compare the rewards of our online algorithm to that of an offline optimum, namely a single independent set of the matroid that maximizes the sum of the weighted rank rewards that arrive over time. This problem is a natural extension of two well-studied streams of earlier work: the first is on online set cover algorithms (in particular for the max coverage version) while the second is on approximately maximizing submodular functions under a matroid constraint. In this paper, we present the first randomized online algorithms for this problem with poly-logarithmic competitive ratio. To do this, we employ the LP formulation of a scaled reward version of the problem. Then we extend a weighted-majority type update rule along with uncrossing properties of tight sets in the matroid polytope to find an approximately optimal fractional LP solution. We use the fractional solution values as probabilities for a online randomized rounding algorithm. To show that our rounding produces a sufficiently large reward independent set, we prove and use new covering properties for randomly rounded fractional solutions in the matroid polytope that may be of independent interest. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1205.1477v1-abstract-full').style.display = 'none'; document.getElementById('1205.1477v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 May, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> F.2.2 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1204.5810">arXiv:1204.5810</a> <span> [<a href="https://arxiv.org/pdf/1204.5810">pdf</a>, <a href="https://arxiv.org/format/1204.5810">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> Geometry of Online Packing Linear Programs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Molinaro%2C+M">Marco Molinaro</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1204.5810v1-abstract-short" style="display: inline;"> We consider packing LP's with $m$ rows where all constraint coefficients are normalized to be in the unit interval. The n columns arrive in random order and the goal is to set the corresponding decision variables irrevocably when they arrive so as to obtain a feasible solution maximizing the expected reward. Previous (1 - 蔚)-competitive algorithms require the right-hand side of the LP to be Omega(… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.5810v1-abstract-full').style.display = 'inline'; document.getElementById('1204.5810v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1204.5810v1-abstract-full" style="display: none;"> We consider packing LP's with $m$ rows where all constraint coefficients are normalized to be in the unit interval. The n columns arrive in random order and the goal is to set the corresponding decision variables irrevocably when they arrive so as to obtain a feasible solution maximizing the expected reward. Previous (1 - 蔚)-competitive algorithms require the right-hand side of the LP to be Omega((m/蔚^2) log (n/蔚)), a bound that worsens with the number of columns and rows. However, the dependence on the number of columns is not required in the single-row case and known lower bounds for the general case are also independent of n. Our goal is to understand whether the dependence on n is required in the multi-row case, making it fundamentally harder than the single-row version. We refute this by exhibiting an algorithm which is (1 - 蔚)-competitive as long as the right-hand sides are Omega((m^2/蔚^2) log (m/蔚)). Our techniques refine previous PAC-learning based approaches which interpret the online decisions as linear classifications of the columns based on sampled dual prices. The key ingredient of our improvement comes from a non-standard covering argument together with the realization that only when the columns of the LP belong to few 1-d subspaces we can obtain small such covers; bounding the size of the cover constructed also relies on the geometry of linear classifiers. General packing LP's are handled by perturbing the input columns, which can be seen as making the learning problem more robust. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.5810v1-abstract-full').style.display = 'none'; document.getElementById('1204.5810v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 April, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2012. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1203.3578">arXiv:1203.3578</a> <span> [<a href="https://arxiv.org/pdf/1203.3578">pdf</a>, <a href="https://arxiv.org/format/1203.3578">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Iterative rounding approximation algorithms for degree-bounded node-connectivity network design </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Fukunaga%2C+T">Takuro Fukunaga</a>, <a href="/search/cs?searchtype=author&query=Nutov%2C+Z">Zeev Nutov</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1203.3578v4-abstract-short" style="display: inline;"> We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset LP relaxation for this problem. For directed graphs and $k$-out-connectivity requirements from a root, our algorithm computes a solution that is a 2-approximation on the cost, and th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1203.3578v4-abstract-full').style.display = 'inline'; document.getElementById('1203.3578v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1203.3578v4-abstract-full" style="display: none;"> We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset LP relaxation for this problem. For directed graphs and $k$-out-connectivity requirements from a root, our algorithm computes a solution that is a 2-approximation on the cost, and the degree of each node $v$ in the solution is at most $2b(v) + O(k)$ where $b(v)$ is the degree upper bound on $v$. For undirected graphs and element-connectivity requirements with maximum connectivity requirement $k$, our algorithm computes a solution that is a $4$-approximation on the cost, and the degree of each node $v$ in the solution is at most $4b(v)+O(k)$. These ratios improve the previous $O(\log k)$-approximation on the cost and $O(2^k b(v))$ approximation on the degrees. Our algorithms can be used to improve approximation ratios for other node-connectivity problems such as undirected $k$-out-connectivity, directed and undirected $k$-connectivity, and undirected rooted $k$-connectivity and subset $k$-connectivity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1203.3578v4-abstract-full').style.display = 'none'; document.getElementById('1203.3578v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 August, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 March, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">A preliminary version of this paper appeared in proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2012)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1110.0990">arXiv:1110.0990</a> <span> [<a href="https://arxiv.org/pdf/1110.0990">pdf</a>, <a href="https://arxiv.org/ps/1110.0990">ps</a>, <a href="https://arxiv.org/format/1110.0990">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> The Query-commit Problem </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Molinaro%2C+M">Marco Molinaro</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1110.0990v1-abstract-short" style="display: inline;"> In the query-commit problem we are given a graph where edges have distinct probabilities of existing. It is possible to query the edges of the graph, and if the queried edge exists then its endpoints are irrevocably matched. The goal is to find a querying strategy which maximizes the expected size of the matching obtained. This stochastic matching setup is motivated by applications in kidney excha… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1110.0990v1-abstract-full').style.display = 'inline'; document.getElementById('1110.0990v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1110.0990v1-abstract-full" style="display: none;"> In the query-commit problem we are given a graph where edges have distinct probabilities of existing. It is possible to query the edges of the graph, and if the queried edge exists then its endpoints are irrevocably matched. The goal is to find a querying strategy which maximizes the expected size of the matching obtained. This stochastic matching setup is motivated by applications in kidney exchanges and online dating. In this paper we address the query-commit problem from both theoretical and experimental perspectives. First, we show that a simple class of edges can be queried without compromising the optimality of the strategy. This property is then used to obtain in polynomial time an optimal querying strategy when the input graph is sparse. Next we turn our attentions to the kidney exchange application, focusing on instances modeled over real data from existing exchange programs. We prove that, as the number of nodes grows, almost every instance admits a strategy which matches almost all nodes. This result supports the intuition that more exchanges are possible on a larger pool of patient/donors and gives theoretical justification for unifying the existing exchange programs. Finally, we evaluate experimentally different querying strategies over kidney exchange instances. We show that even very simple heuristics perform fairly well, being within 1.5% of an optimal clairvoyant strategy, that knows in advance the edges in the graph. In such a time-sensitive application, this result motivates the use of committing strategies. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1110.0990v1-abstract-full').style.display = 'none'; document.getElementById('1110.0990v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 October, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2011. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1102.5450">arXiv:1102.5450</a> <span> [<a href="https://arxiv.org/pdf/1102.5450">pdf</a>, <a href="https://arxiv.org/format/1102.5450">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Minimum Makespan Multi-vehicle Dial-a-Ride </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Goertz%2C+I+L">Inge Li Goertz</a>, <a href="/search/cs?searchtype=author&query=Nagarajan%2C+V">Viswanath Nagarajan</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1102.5450v1-abstract-short" style="display: inline;"> Dial a ride problems consist of a metric space (denoting travel time between vertices) and a set of m objects represented as source-destination pairs, where each object requires to be moved from its source to destination vertex. We consider the multi-vehicle Dial a ride problem, with each vehicle having capacity k and its own depot-vertex, where the objective is to minimize the maximum completion… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.5450v1-abstract-full').style.display = 'inline'; document.getElementById('1102.5450v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1102.5450v1-abstract-full" style="display: none;"> Dial a ride problems consist of a metric space (denoting travel time between vertices) and a set of m objects represented as source-destination pairs, where each object requires to be moved from its source to destination vertex. We consider the multi-vehicle Dial a ride problem, with each vehicle having capacity k and its own depot-vertex, where the objective is to minimize the maximum completion time (makespan) of the vehicles. We study the "preemptive" version of the problem, where an object may be left at intermediate vertices and transported by more than one vehicle, while being moved from source to destination. Our main results are an O(log^3 n)-approximation algorithm for preemptive multi-vehicle Dial a ride, and an improved O(log t)-approximation for its special case when there is no capacity constraint. We also show that the approximation ratios improve by a log-factor when the underlying metric is induced by a fixed-minor-free graph. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.5450v1-abstract-full').style.display = 'none'; document.getElementById('1102.5450v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 February, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 1 figure. Preliminary version appeared in ESA 2009</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1102.3749">arXiv:1102.3749</a> <span> [<a href="https://arxiv.org/pdf/1102.3749">pdf</a>, <a href="https://arxiv.org/ps/1102.3749">ps</a>, <a href="https://arxiv.org/format/1102.3749">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Approximation Algorithms for Correlated Knapsacks and Non-Martingale Bandits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gupta%2C+A">Anupam Gupta</a>, <a href="/search/cs?searchtype=author&query=Krishnaswamy%2C+R">Ravishankar Krishnaswamy</a>, <a href="/search/cs?searchtype=author&query=Molinaro%2C+M">Marco Molinaro</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1102.3749v1-abstract-short" style="display: inline;"> In the stochastic knapsack problem, we are given a knapsack of size B, and a set of jobs whose sizes and rewards are drawn from a known probability distribution. However, we know the actual size and reward only when the job completes. How should we schedule jobs to maximize the expected total reward? We know O(1)-approximations when we assume that (i) rewards and sizes are independent random varia… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.3749v1-abstract-full').style.display = 'inline'; document.getElementById('1102.3749v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1102.3749v1-abstract-full" style="display: none;"> In the stochastic knapsack problem, we are given a knapsack of size B, and a set of jobs whose sizes and rewards are drawn from a known probability distribution. However, we know the actual size and reward only when the job completes. How should we schedule jobs to maximize the expected total reward? We know O(1)-approximations when we assume that (i) rewards and sizes are independent random variables, and (ii) we cannot prematurely cancel jobs. What can we say when either or both of these assumptions are changed? The stochastic knapsack problem is of interest in its own right, but techniques developed for it are applicable to other stochastic packing problems. Indeed, ideas for this problem have been useful for budgeted learning problems, where one is given several arms which evolve in a specified stochastic fashion with each pull, and the goal is to pull the arms a total of B times to maximize the reward obtained. Much recent work on this problem focus on the case when the evolution of the arms follows a martingale, i.e., when the expected reward from the future is the same as the reward at the current state. What can we say when the rewards do not form a martingale? In this paper, we give constant-factor approximation algorithms for the stochastic knapsack problem with correlations and/or cancellations, and also for budgeted learning problems where the martingale condition is not satisfied. Indeed, we can show that previously proposed LP relaxations have large integrality gaps. We propose new time-indexed LP relaxations, and convert the fractional solutions into distributions over strategies, and then use the LP values and the time ordering information from these strategies to devise a randomized adaptive scheduling algorithm. We hope our LP formulation and decomposition methods may provide a new way to address other correlated bandit problems with more general contexts. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.3749v1-abstract-full').style.display = 'none'; document.getElementById('1102.3749v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 February, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2011. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1012.4962">arXiv:1012.4962</a> <span> [<a href="https://arxiv.org/pdf/1012.4962">pdf</a>, <a href="https://arxiv.org/ps/1012.4962">ps</a>, <a href="https://arxiv.org/format/1012.4962">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Robust and MaxMin Optimization under Matroid and Knapsack Uncertainty Sets </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gupta%2C+A">Anupam Gupta</a>, <a href="/search/cs?searchtype=author&query=Nagarajan%2C+V">Viswanath Nagarajan</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1012.4962v2-abstract-short" style="display: inline;"> Consider the following problem: given a set system (U,I) and an edge-weighted graph G = (U, E) on the same universe U, find the set A in I such that the Steiner tree cost with terminals A is as large as possible: "which set in I is the most difficult to connect up?" This is an example of a max-min problem: find the set A in I such that the value of some minimization (covering) problem is as large… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1012.4962v2-abstract-full').style.display = 'inline'; document.getElementById('1012.4962v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1012.4962v2-abstract-full" style="display: none;"> Consider the following problem: given a set system (U,I) and an edge-weighted graph G = (U, E) on the same universe U, find the set A in I such that the Steiner tree cost with terminals A is as large as possible: "which set in I is the most difficult to connect up?" This is an example of a max-min problem: find the set A in I such that the value of some minimization (covering) problem is as large as possible. In this paper, we show that for certain covering problems which admit good deterministic online algorithms, we can give good algorithms for max-min optimization when the set system I is given by a p-system or q-knapsacks or both. This result is similar to results for constrained maximization of submodular functions. Although many natural covering problems are not even approximately submodular, we show that one can use properties of the online algorithm as a surrogate for submodularity. Moreover, we give stronger connections between max-min optimization and two-stage robust optimization, and hence give improved algorithms for robust versions of various covering problems, for cases where the uncertainty sets are given by p-systems and q-knapsacks. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1012.4962v2-abstract-full').style.display = 'none'; document.getElementById('1012.4962v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 February, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 December, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages. Preliminary version combining this paper and http://arxiv.org/abs/0912.1045 appeared in ICALP 2010</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1012.1850">arXiv:1012.1850</a> <span> [<a href="https://arxiv.org/pdf/1012.1850">pdf</a>, <a href="https://arxiv.org/format/1012.1850">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> </div> </div> <p class="title is-5 mathjax"> Capacitated Vehicle Routing with Non-Uniform Speeds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gortz%2C+I+L">Inge Li Gortz</a>, <a href="/search/cs?searchtype=author&query=Molinaro%2C+M">Marco Molinaro</a>, <a href="/search/cs?searchtype=author&query=Nagarajan%2C+V">Viswanath Nagarajan</a>, <a href="/search/cs?searchtype=author&query=Ravi%2C+R">R. Ravi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1012.1850v1-abstract-short" style="display: inline;"> The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple vehicles having non-uniform speeds (that we call Heterogenous CVRP), and present a constant-factor approximation algorithm. The technical heart of our result lies… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1012.1850v1-abstract-full').style.display = 'inline'; document.getElementById('1012.1850v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1012.1850v1-abstract-full" style="display: none;"> The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple vehicles having non-uniform speeds (that we call Heterogenous CVRP), and present a constant-factor approximation algorithm. The technical heart of our result lies in achieving a constant approximation to the following TSP variant (called Heterogenous TSP). Given a metric denoting distances between vertices, a depot r containing k vehicles with possibly different speeds, the goal is to find a tour for each vehicle (starting and ending at r), so that every vertex is covered in some tour and the maximum completion time is minimized. This problem is precisely Heterogenous CVRP when vehicles are uncapacitated. The presence of non-uniform speeds introduces difficulties for employing standard tour-splitting techniques. In order to get a better understanding of this technique in our context, we appeal to ideas from the 2-approximation for scheduling in parallel machine of Lenstra et al.. This motivates the introduction of a new approximate MST construction called Level-Prim, which is related to Light Approximate Shortest-path Trees. The last component of our algorithm involves partitioning the Level-Prim tree and matching the resulting parts to vehicles. This decomposition is more subtle than usual since now we need to enforce correlation between the size of the parts and their distances to the depot. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1012.1850v1-abstract-full').style.display = 'none'; document.getElementById('1012.1850v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 December, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2010. </p> </li> </ol> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Ravi%2C+R&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Ravi%2C+R&start=0" 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