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name="abstracts" type="radio" value="hide"> <label for="abstracts-1">Hide abstracts</label></li></ul> </div> <div class="box field is-grouped is-grouped-multiline level-item"> <div class="control"> <span class="select is-small"> <select id="size" name="size"><option value="25">25</option><option selected value="50">50</option><option value="100">100</option><option value="200">200</option></select> </span> <label for="size">results per page</label>. </div> <div class="control"> <label for="order">Sort results by</label> <span class="select is-small"> <select id="order" name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <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/2502.15320">arXiv:2502.15320</a> <span> [<a href="https://arxiv.org/pdf/2502.15320">pdf</a>, <a href="https://arxiv.org/ps/2502.15320">ps</a>, <a href="https://arxiv.org/format/2502.15320">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="Distributed, Parallel, and Cluster Computing">cs.DC</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"> Adversarially-Robust Gossip Algorithms for Approximate Quantile and Mean Computations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Haeupler%2C+B">Bernhard Haeupler</a>, <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="2502.15320v1-abstract-short" style="display: inline;"> This paper presents the first gossip algorithms that are robust to adversarial corruptions. Gossip algorithms distribute information in a scalable and efficient way by having random pairs of nodes exchange small messages. Value aggregation problems are of particular interest in this setting as they occur frequently in practice and many elegant algorithms have been proposed for computing aggregates… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.15320v1-abstract-full').style.display = 'inline'; document.getElementById('2502.15320v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2502.15320v1-abstract-full" style="display: none;"> This paper presents the first gossip algorithms that are robust to adversarial corruptions. Gossip algorithms distribute information in a scalable and efficient way by having random pairs of nodes exchange small messages. Value aggregation problems are of particular interest in this setting as they occur frequently in practice and many elegant algorithms have been proposed for computing aggregates and statistics such as averages and quantiles. An important and well-studied advantage of gossip algorithms is their robustness to message delays, network churn, and unreliable message transmissions. These crucial robustness guarantees however only hold if all nodes follow the protocol and no messages are corrupted. In this paper, we remedy this by providing a framework to model both adversarial participants and message corruptions in gossip-style communications by allowing an adversary to control a small fraction of the nodes or corrupt messages arbitrarily. Despite this very powerful and general corruption model, we show that one can design robust gossip algorithms for many important aggregation problems. Our algorithms guarantee that almost all nodes converge to an approximately correct answer with optimal efficiency and essentially as fast as without corruptions. The design of adversarially-robust gossip algorithms poses completely new challenges. Despite this, our algorithms remain very simple variations of known non-robust algorithms with often only subtle changes to avoid non-compliant nodes gaining too much influence over outcomes. While our algorithms remain simple, their analysis is much more complex and often requires a completely different approach than the non-adversarial setting. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2502.15320v1-abstract-full').style.display = 'none'; document.getElementById('2502.15320v1-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2025. </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/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> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a 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