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graph</title> <meta name="description" content="Search results for: sparse graph"> <meta name="keywords" content="sparse graph"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler 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style="font-size:.9rem"><span class="badge badge-info">630</span> An Improved Method to Compute Sparse Graphs for Traveling Salesman Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20Wang">Y. Wang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is <em>O</em>(<em>CN</em><sub>max</sub><em>n</em><sup>2</sup>) where <em>C</em> is the iterations, <em>N</em><sub>max</sub> is the maximum number of frequency quadrilaterals containing each edge and <em>n</em> is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5<em>n</em> edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=frequency%20quadrilateral" title="frequency quadrilateral">frequency quadrilateral</a>, <a href="https://publications.waset.org/abstracts/search?q=iterative%20algorithm" title=" iterative algorithm"> iterative algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse%20graph" title=" sparse graph"> sparse graph</a>, <a href="https://publications.waset.org/abstracts/search?q=traveling%20salesman%20problem" title=" traveling salesman problem"> traveling salesman problem</a> </p> <a href="https://publications.waset.org/abstracts/82737/an-improved-method-to-compute-sparse-graphs-for-traveling-salesman-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/82737.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">233</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">629</span> Topological Indices of Some Graph Operations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=U.%20Mary">U. Mary </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let be a graph with a finite, nonempty set of objects called vertices together with a set of unordered pairs of distinct vertices of called edges. The vertex set is denoted by and the edge set by. Given two graphs and the wiener index of, wiener index for the splitting graph of a graph, the first Zagreb index of and its splitting graph, the 3-steiner wiener index of, the 3-steiner wiener index of a special graph are explored in this paper. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=complementary%20prism%20graph" title="complementary prism graph">complementary prism graph</a>, <a href="https://publications.waset.org/abstracts/search?q=first%20Zagreb%20index" title=" first Zagreb index"> first Zagreb index</a>, <a href="https://publications.waset.org/abstracts/search?q=neighborhood%20corona%20graph" title=" neighborhood corona graph"> neighborhood corona graph</a>, <a href="https://publications.waset.org/abstracts/search?q=steiner%20distance" title=" steiner distance"> steiner distance</a>, <a href="https://publications.waset.org/abstracts/search?q=splitting%20graph" title=" splitting graph"> splitting graph</a>, <a href="https://publications.waset.org/abstracts/search?q=steiner%20wiener%20index" title=" steiner wiener index"> steiner wiener index</a>, <a href="https://publications.waset.org/abstracts/search?q=wiener%20index" title=" wiener index"> wiener index</a> </p> <a href="https://publications.waset.org/abstracts/16774/topological-indices-of-some-graph-operations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16774.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">570</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">628</span> Survey Paper on Graph Coloring Problem and Its Application</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Prateek%20Chharia">Prateek Chharia</a>, <a href="https://publications.waset.org/abstracts/search?q=Biswa%20Bhusan%20Ghosh"> Biswa Bhusan Ghosh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Graph coloring is one of the prominent concepts in graph coloring. It can be defined as a coloring of the various regions of the graph such that all the constraints are fulfilled. In this paper various graphs coloring approaches like greedy coloring, Heuristic search for maximum independent set and graph coloring using edge table is described. Graph coloring can be used in various real time applications like student time tabling generation, Sudoku as a graph coloring problem, GSM phone network. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20coloring" title="graph coloring">graph coloring</a>, <a href="https://publications.waset.org/abstracts/search?q=greedy%20coloring" title=" greedy coloring"> greedy coloring</a>, <a href="https://publications.waset.org/abstracts/search?q=heuristic%20search" title=" heuristic search"> heuristic search</a>, <a href="https://publications.waset.org/abstracts/search?q=edge%20table" title=" edge table"> edge table</a>, <a href="https://publications.waset.org/abstracts/search?q=sudoku%20as%20a%20graph%20coloring%20problem" title=" sudoku as a graph coloring problem"> sudoku as a graph coloring problem</a> </p> <a href="https://publications.waset.org/abstracts/19691/survey-paper-on-graph-coloring-problem-and-its-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19691.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">539</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">627</span> Non-Local Simultaneous Sparse Unmixing for Hyperspectral Data</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fanqiang%20Kong">Fanqiang Kong</a>, <a href="https://publications.waset.org/abstracts/search?q=Chending%20Bian"> Chending Bian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Sparse unmixing is a promising approach in a semisupervised fashion by assuming that the observed pixels of a hyperspectral image can be expressed in the form of linear combination of only a few pure spectral signatures (end members) in an available spectral library. However, the sparse unmixing problem still remains a great challenge at finding the optimal subset of endmembers for the observed data from a large standard spectral library, without considering the spatial information. Under such circumstances, a sparse unmixing algorithm termed as non-local simultaneous sparse unmixing (NLSSU) is presented. In NLSSU, the non-local simultaneous sparse representation method for endmember selection of sparse unmixing, is used to finding the optimal subset of endmembers for the similar image patch set in the hyperspectral image. And then, the non-local means method, as a regularizer for abundance estimation of sparse unmixing, is used to exploit the abundance image non-local self-similarity. Experimental results on both simulated and real data demonstrate that NLSSU outperforms the other algorithms, with a better spectral unmixing accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hyperspectral%20unmixing" title="hyperspectral unmixing">hyperspectral unmixing</a>, <a href="https://publications.waset.org/abstracts/search?q=simultaneous%20sparse%20representation" title=" simultaneous sparse representation"> simultaneous sparse representation</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse%20regression" title=" sparse regression"> sparse regression</a>, <a href="https://publications.waset.org/abstracts/search?q=non-local%20means" title=" non-local means"> non-local means</a> </p> <a href="https://publications.waset.org/abstracts/71689/non-local-simultaneous-sparse-unmixing-for-hyperspectral-data" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/71689.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">245</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">626</span> A New Graph Theoretic Problem with Ample Practical Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mehmet%20Hakan%20Karaata">Mehmet Hakan Karaata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=algorithm" title="algorithm">algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=cycle" title=" cycle"> cycle</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20algorithm" title=" graph algorithm"> graph algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20theory" title=" graph theory"> graph theory</a>, <a href="https://publications.waset.org/abstracts/search?q=network%20structuring" title=" network structuring"> network structuring</a> </p> <a href="https://publications.waset.org/abstracts/67285/a-new-graph-theoretic-problem-with-ample-practical-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67285.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">386</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">625</span> Complete Tripartite Graphs with Spanning Maximal Planar Subgraphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Severino%20Gervacio">Severino Gervacio</a>, <a href="https://publications.waset.org/abstracts/search?q=Velimor%20Almonte"> Velimor Almonte</a>, <a href="https://publications.waset.org/abstracts/search?q=Emmanuel%20Natalio"> Emmanuel Natalio</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A simple graph is planar if it there is a way of drawing it in the plane without edge crossings. A planar graph which is not a proper spanning subgraph of another planar graph is a maximal planar graph. We prove that for complete tripartite graphs of order at most 9, the only ones that contain a spanning maximal planar subgraph are K1,1,1, K2,2,2, K2,3,3, and K3,3,3. The main result gives a necessary and sufficient condition for the complete tripartite graph Kx,y,z to contain a spanning maximal planar subgraph. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=complete%20tripartite%20graph" title="complete tripartite graph">complete tripartite graph</a>, <a href="https://publications.waset.org/abstracts/search?q=graph" title=" graph"> graph</a>, <a href="https://publications.waset.org/abstracts/search?q=maximal%20planar%20graph" title=" maximal planar graph"> maximal planar graph</a>, <a href="https://publications.waset.org/abstracts/search?q=planar%20graph" title=" planar graph"> planar graph</a>, <a href="https://publications.waset.org/abstracts/search?q=subgraph" title=" subgraph"> subgraph</a> </p> <a href="https://publications.waset.org/abstracts/59157/complete-tripartite-graphs-with-spanning-maximal-planar-subgraphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59157.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">381</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">624</span> Efficient Filtering of Graph Based Data Using Graph Partitioning</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nileshkumar%20Vaishnav">Nileshkumar Vaishnav</a>, <a href="https://publications.waset.org/abstracts/search?q=Aditya%20Tatu"> Aditya Tatu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20signal%20processing" title="graph signal processing">graph signal processing</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20partitioning" title=" graph partitioning"> graph partitioning</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20filtering%20on%20graphs" title=" inverse filtering on graphs"> inverse filtering on graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=algebraic%20signal%20processing" title=" algebraic signal processing"> algebraic signal processing</a> </p> <a href="https://publications.waset.org/abstracts/59397/efficient-filtering-of-graph-based-data-using-graph-partitioning" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59397.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">311</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">623</span> Improvement a Lower Bound of Energy for Some Family of Graphs, Related to Determinant of Adjacency Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saieed%20%20Akbari">Saieed Akbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Yousef%20Bagheri"> Yousef Bagheri</a>, <a href="https://publications.waset.org/abstracts/search?q=Amir%20Hossein%20Ghodrati"> Amir Hossein Ghodrati</a>, <a href="https://publications.waset.org/abstracts/search?q=Sima%20Saadat%20Akhtar"> Sima Saadat Akhtar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let G be a simple graph with the vertex set V (G) and with the adjacency matrix A (G). The energy E (G) of G is defined to be the sum of the absolute values of all eigenvalues of A (G). Also let n and m be number of edges and vertices of the graph respectively. A regular graph is a graph where each vertex has the same number of neighbours. Given a graph G, its line graph L(G) is a graph such that each vertex of L(G) represents an edge of G; and two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint in G. In this paper we show that for every regular graphs and also for every line graphs such that (G) 3 we have, E(G) 2nm + n 1. Also at the other part of the paper we prove that 2 (G) E(G) for an arbitrary graph G. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=eigenvalues" title="eigenvalues">eigenvalues</a>, <a href="https://publications.waset.org/abstracts/search?q=energy" title=" energy"> energy</a>, <a href="https://publications.waset.org/abstracts/search?q=line%20graphs" title=" line graphs"> line graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=matching%20number" title=" matching number"> matching number</a> </p> <a href="https://publications.waset.org/abstracts/99652/improvement-a-lower-bound-of-energy-for-some-family-of-graphs-related-to-determinant-of-adjacency-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99652.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">232</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">622</span> Graph Similarity: Algebraic Model and Its Application to Nonuniform Signal Processing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nileshkumar%20Vishnav">Nileshkumar Vishnav</a>, <a href="https://publications.waset.org/abstracts/search?q=Aditya%20Tatu"> Aditya Tatu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20signal%20processing" title="graph signal processing">graph signal processing</a>, <a href="https://publications.waset.org/abstracts/search?q=algebraic%20signal%20processing" title=" algebraic signal processing"> algebraic signal processing</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20similarity" title=" graph similarity"> graph similarity</a>, <a href="https://publications.waset.org/abstracts/search?q=isospectral%20graphs" title=" isospectral graphs"> isospectral graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=nonuniform%20signal%20processing" title=" nonuniform signal processing"> nonuniform signal processing</a> </p> <a href="https://publications.waset.org/abstracts/59404/graph-similarity-algebraic-model-and-its-application-to-nonuniform-signal-processing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59404.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">352</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">621</span> Sparse Principal Component Analysis: A Least Squares Approximation Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Giovanni%20Merola">Giovanni Merola</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective function. This approach differs from others because it preserves PCA's original optimality: uncorrelatedness of the components and least squares approximation of the data. To identify the best subset of non-zero loadings we propose a branch-and-bound search and an iterative elimination algorithm. This last algorithm finds sparse solutions with large loadings and can be run without specifying the cardinality of the loadings and the number of components to compute in advance. We give thorough comparisons with the existing sparse PCA methods and several examples on real datasets. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=SPCA" title="SPCA">SPCA</a>, <a href="https://publications.waset.org/abstracts/search?q=uncorrelated%20components" title=" uncorrelated components"> uncorrelated components</a>, <a href="https://publications.waset.org/abstracts/search?q=branch-and-bound" title=" branch-and-bound"> branch-and-bound</a>, <a href="https://publications.waset.org/abstracts/search?q=backward%20elimination" title=" backward elimination"> backward elimination</a> </p> <a href="https://publications.waset.org/abstracts/14630/sparse-principal-component-analysis-a-least-squares-approximation-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14630.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">381</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">620</span> Metric Dimension on Line Graph of Honeycomb Networks</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Hussain">M. Hussain</a>, <a href="https://publications.waset.org/abstracts/search?q=Aqsa%20Farooq"> Aqsa Farooq</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let G = (V,E) be a connected graph and distance between any two vertices a and b in G is a−b geodesic and is denoted by d(a, b). A set of vertices W resolves a graph G if each vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G. In this paper line graph of honeycomb network has been derived and then we calculated the metric dimension on line graph of honeycomb network. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Resolving%20set" title="Resolving set">Resolving set</a>, <a href="https://publications.waset.org/abstracts/search?q=Metric%20dimension" title=" Metric dimension"> Metric dimension</a>, <a href="https://publications.waset.org/abstracts/search?q=Honeycomb%20network" title=" Honeycomb network"> Honeycomb network</a>, <a href="https://publications.waset.org/abstracts/search?q=Line%20graph" title=" Line graph"> Line graph</a> </p> <a href="https://publications.waset.org/abstracts/101558/metric-dimension-on-line-graph-of-honeycomb-networks" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/101558.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">200</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">619</span> Speedup Breadth-First Search by Graph Ordering</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Qiuyi%20Lyu">Qiuyi Lyu</a>, <a href="https://publications.waset.org/abstracts/search?q=Bin%20Gong"> Bin Gong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Breadth-First Search(BFS) is a core graph algorithm that is widely used for graph analysis. As it is frequently used in many graph applications, improve the BFS performance is essential. In this paper, we present a graph ordering method that could reorder the graph nodes to achieve better data locality, thus, improving the BFS performance. Our method is based on an observation that the sibling relationships will dominate the cache access pattern during the BFS traversal. Therefore, we propose a frequency-based model to construct the graph order. First, we optimize the graph order according to the nodes’ visit frequency. Nodes with high visit frequency will be processed in priority. Second, we try to maximize the child nodes overlap layer by layer. As it is proved to be NP-hard, we propose a heuristic method that could greatly reduce the preprocessing overheads. We conduct extensive experiments on 16 real-world datasets. The result shows that our method could achieve comparable performance with the state-of-the-art methods while the graph ordering overheads are only about 1/15. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=breadth-first%20search" title="breadth-first search">breadth-first search</a>, <a href="https://publications.waset.org/abstracts/search?q=BFS" title=" BFS"> BFS</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20ordering" title=" graph ordering"> graph ordering</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20algorithm" title=" graph algorithm"> graph algorithm</a> </p> <a href="https://publications.waset.org/abstracts/136790/speedup-breadth-first-search-by-graph-ordering" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/136790.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">138</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">618</span> A Study of Families of Bistar and Corona Product of Graph: Reverse Topological Indices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gowtham%20Kalkere%20Jayanna">Gowtham Kalkere Jayanna</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamad%20Nazri%20Husin"> Mohamad Nazri Husin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Graph theory, chemistry, and technology are all combined in cheminformatics. The structure and physiochemical properties of organic substances are linked using some useful graph invariants and the corresponding molecular graph. In this paper, we study specific reverse topological indices such as the reverse sum-connectivity index, the reverse Zagreb index, the reverse arithmetic-geometric, and the geometric-arithmetic, the reverse Sombor, the reverse Nirmala indices for the bistar graphs B (n: m) and the corona product Kₘ∘Kₙ', where Kₙ' Represent the complement of a complete graph Kₙ. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=reverse%20topological%20indices" title="reverse topological indices">reverse topological indices</a>, <a href="https://publications.waset.org/abstracts/search?q=bistar%20graph" title=" bistar graph"> bistar graph</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20corona%20product" title=" the corona product"> the corona product</a>, <a href="https://publications.waset.org/abstracts/search?q=graph" title=" graph"> graph</a> </p> <a href="https://publications.waset.org/abstracts/166540/a-study-of-families-of-bistar-and-corona-product-of-graph-reverse-topological-indices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/166540.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">97</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">617</span> On the Zeros of the Degree Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20R.%20Nayaka">S. R. Nayaka</a>, <a href="https://publications.waset.org/abstracts/search?q=Putta%20Swamy"> Putta Swamy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=degree%20polynomial" title="degree polynomial">degree polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=regular%20graph" title=" regular graph"> regular graph</a>, <a href="https://publications.waset.org/abstracts/search?q=minimum%20and%20maximum%20degree" title=" minimum and maximum degree"> minimum and maximum degree</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20operations" title=" graph operations"> graph operations</a> </p> <a href="https://publications.waset.org/abstracts/56602/on-the-zeros-of-the-degree-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56602.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">249</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">616</span> From Convexity in Graphs to Polynomial Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ladznar%20S.%20Laja">Ladznar S. Laja</a>, <a href="https://publications.waset.org/abstracts/search?q=Rosalio%20G.%20Artes"> Rosalio G. Artes</a>, <a href="https://publications.waset.org/abstracts/search?q=Jr."> Jr.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20subgraph" title="convex subgraph">convex subgraph</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20index" title=" convex index"> convex index</a>, <a href="https://publications.waset.org/abstracts/search?q=generating%20function" title=" generating function"> generating function</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20ring" title=" polynomial ring"> polynomial ring</a> </p> <a href="https://publications.waset.org/abstracts/9019/from-convexity-in-graphs-to-polynomial-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9019.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">215</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">615</span> Sparsity Order Selection and Denoising in Compressed Sensing Framework</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mahdi%20Shamsi">Mahdi Shamsi</a>, <a href="https://publications.waset.org/abstracts/search?q=Tohid%20Yousefi%20Rezaii"> Tohid Yousefi Rezaii</a>, <a href="https://publications.waset.org/abstracts/search?q=Siavash%20Eftekharifar"> Siavash Eftekharifar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Compressed sensing (CS) is a new powerful mathematical theory concentrating on sparse signals which is widely used in signal processing. The main idea is to sense sparse signals by far fewer measurements than the Nyquist sampling rate, but the reconstruction process becomes nonlinear and more complicated. Common dilemma in sparse signal recovery in CS is the lack of knowledge about sparsity order of the signal, which can be viewed as model order selection procedure. In this paper, we address the problem of sparsity order estimation in sparse signal recovery. This is of main interest in situations where the signal sparsity is unknown or the signal to be recovered is approximately sparse. It is shown that the proposed method also leads to some kind of signal denoising, where the observations are contaminated with noise. Finally, the performance of the proposed approach is evaluated in different scenarios and compared to an existing method, which shows the effectiveness of the proposed method in terms of order selection as well as denoising. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compressed%20sensing" title="compressed sensing">compressed sensing</a>, <a href="https://publications.waset.org/abstracts/search?q=data%20denoising" title=" data denoising"> data denoising</a>, <a href="https://publications.waset.org/abstracts/search?q=model%20order%20selection" title=" model order selection"> model order selection</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse%20representation" title=" sparse representation"> sparse representation</a> </p> <a href="https://publications.waset.org/abstracts/31470/sparsity-order-selection-and-denoising-in-compressed-sensing-framework" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31470.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">483</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">614</span> Performance Analysis and Optimization for Diagonal Sparse Matrix-Vector Multiplication on Machine Learning Unit</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Qiuyu%20Dai">Qiuyu Dai</a>, <a href="https://publications.waset.org/abstracts/search?q=Haochong%20Zhang"> Haochong Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Xiangrong%20Liu"> Xiangrong Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Diagonal sparse matrix-vector multiplication is a well-studied topic in the fields of scientific computing and big data processing. However, when diagonal sparse matrices are stored in DIA format, there can be a significant number of padded zero elements and scattered points, which can lead to a degradation in the performance of the current DIA kernel. This can also lead to excessive consumption of computational and memory resources. In order to address these issues, the authors propose the DIA-Adaptive scheme and its kernel, which leverages the parallel instruction sets on MLU. The researchers analyze the effect of allocating a varying number of threads, clusters, and hardware architectures on the performance of SpMV using different formats. The experimental results indicate that the proposed DIA-Adaptive scheme performs well and offers excellent parallelism. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptive%20method" title="adaptive method">adaptive method</a>, <a href="https://publications.waset.org/abstracts/search?q=DIA" title=" DIA"> DIA</a>, <a href="https://publications.waset.org/abstracts/search?q=diagonal%20sparse%20matrices" title=" diagonal sparse matrices"> diagonal sparse matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=MLU" title=" MLU"> MLU</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse%20matrix-vector%20multiplication" title=" sparse matrix-vector multiplication"> sparse matrix-vector multiplication</a> </p> <a href="https://publications.waset.org/abstracts/161003/performance-analysis-and-optimization-for-diagonal-sparse-matrix-vector-multiplication-on-machine-learning-unit" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/161003.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">135</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">613</span> An Application of Graph Theory to The Electrical Circuit Using Matrix Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Samai%27la%20Abdullahi">Samai'la Abdullahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A graph is a pair of two set and so that a graph is a pictorial representation of a system using two basic element nodes and edges. A node is represented by a circle (either hallo shade) and edge is represented by a line segment connecting two nodes together. In this paper, we present a circuit network in the concept of graph theory application and also circuit models of graph are represented in logical connection method were we formulate matrix method of adjacency and incidence of matrix and application of truth table. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=euler%20circuit%20and%20path" title="euler circuit and path">euler circuit and path</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20representation%20of%20circuit%20networks" title=" graph representation of circuit networks"> graph representation of circuit networks</a>, <a href="https://publications.waset.org/abstracts/search?q=representation%20of%20graph%20models" title=" representation of graph models"> representation of graph models</a>, <a href="https://publications.waset.org/abstracts/search?q=representation%20of%20circuit%20network%20using%20logical%20truth%20table" title=" representation of circuit network using logical truth table"> representation of circuit network using logical truth table</a> </p> <a href="https://publications.waset.org/abstracts/32358/an-application-of-graph-theory-to-the-electrical-circuit-using-matrix-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32358.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">561</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">612</span> Building 1-Well-Covered Graphs by Corona, Join, and Rooted Product of Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vadim%20E.%20Levit">Vadim E. Levit</a>, <a href="https://publications.waset.org/abstracts/search?q=Eugen%20Mandrescu"> Eugen Mandrescu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A graph is well-covered if all its maximal independent sets are of the same size. A well-covered graph is 1-well-covered if deletion of every vertex of the graph leaves it well-covered. It is known that a graph without isolated vertices is 1-well-covered if and only if every two disjoint independent sets are included in two disjoint maximum independent sets. Well-covered graphs are related to combinatorial commutative algebra (e.g., every Cohen-Macaulay graph is well-covered, while each Gorenstein graph without isolated vertices is 1-well-covered). Our intent is to construct several infinite families of 1-well-covered graphs using the following known graph operations: corona, join, and rooted product of graphs. Adopting some known techniques used to advantage for well-covered graphs, one can prove that: if the graph G has no isolated vertices, then the corona of G and H is 1-well-covered if and only if H is a complete graph of order two at least; the join of the graphs G and H is 1-well-covered if and only if G and H have the same independence number and both are 1-well-covered; if H satisfies the property that every three pairwise disjoint independent sets are included in three pairwise disjoint maximum independent sets, then the rooted product of G and H is 1-well-covered, for every graph G. These findings show not only how to generate some more families of 1-well-covered graphs, but also that, to this aim, sometimes, one may use graphs that are not necessarily 1-well-covered. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=maximum%20independent%20set" title="maximum independent set">maximum independent set</a>, <a href="https://publications.waset.org/abstracts/search?q=corona" title=" corona"> corona</a>, <a href="https://publications.waset.org/abstracts/search?q=concatenation" title=" concatenation"> concatenation</a>, <a href="https://publications.waset.org/abstracts/search?q=join" title=" join"> join</a>, <a href="https://publications.waset.org/abstracts/search?q=well-covered%20graph" title=" well-covered graph"> well-covered graph</a> </p> <a href="https://publications.waset.org/abstracts/86859/building-1-well-covered-graphs-by-corona-join-and-rooted-product-of-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86859.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">208</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">611</span> A Transform Domain Function Controlled VSSLMS Algorithm for Sparse System Identification</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cemil%20Turan">Cemil Turan</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Shukri%20Salman"> Mohammad Shukri Salman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The convergence rate of the least-mean-square (LMS) algorithm deteriorates if the input signal to the filter is correlated. In a system identification problem, this convergence rate can be improved if the signal is white and/or if the system is sparse. We recently proposed a sparse transform domain LMS-type algorithm that uses a variable step-size for a sparse system identification. The proposed algorithm provided high performance even if the input signal is highly correlated. In this work, we investigate the performance of the proposed TD-LMS algorithm for a large number of filter tap which is also a critical issue for standard LMS algorithm. Additionally, the optimum value of the most important parameter is calculated for all experiments. Moreover, the convergence analysis of the proposed algorithm is provided. The performance of the proposed algorithm has been compared to different algorithms in a sparse system identification setting of different sparsity levels and different number of filter taps. Simulations have shown that the proposed algorithm has prominent performance compared to the other algorithms. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptive%20filtering" title="adaptive filtering">adaptive filtering</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse%20system%20identification" title=" sparse system identification"> sparse system identification</a>, <a href="https://publications.waset.org/abstracts/search?q=TD-LMS%20algorithm" title=" TD-LMS algorithm"> TD-LMS algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=VSSLMS%20algorithm" title=" VSSLMS algorithm"> VSSLMS algorithm</a> </p> <a href="https://publications.waset.org/abstracts/72335/a-transform-domain-function-controlled-vsslms-algorithm-for-sparse-system-identification" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72335.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">360</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">610</span> Nullity of t-Tupple Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khidir%20R.%20Sharaf">Khidir R. Sharaf</a>, <a href="https://publications.waset.org/abstracts/search?q=Didar%20A.%20Ali"> Didar A. Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The nullity η (G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f (w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced sub-graph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the end vertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs. Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20theory" title="graph theory">graph theory</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20spectra" title=" graph spectra"> graph spectra</a>, <a href="https://publications.waset.org/abstracts/search?q=nullity%20of%20graphs" title=" nullity of graphs"> nullity of graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=statistic" title=" statistic"> statistic</a> </p> <a href="https://publications.waset.org/abstracts/4759/nullity-of-t-tupple-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4759.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">239</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">609</span> Development of a Few-View Computed Tomographic Reconstruction Algorithm Using Multi-Directional Total Variation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chia%20Jui%20Hsieh">Chia Jui Hsieh</a>, <a href="https://publications.waset.org/abstracts/search?q=Jyh%20Cheng%20Chen"> Jyh Cheng Chen</a>, <a href="https://publications.waset.org/abstracts/search?q=Chih%20Wei%20Kuo"> Chih Wei Kuo</a>, <a href="https://publications.waset.org/abstracts/search?q=Ruei%20Teng%20Wang"> Ruei Teng Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=Woei%20Chyn%20Chu"> Woei Chyn Chu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Compressed sensing (CS) based computed tomographic (CT) reconstruction algorithm utilizes total variation (TV) to transform CT image into sparse domain and minimizes L1-norm of sparse image for reconstruction. Different from the traditional CS based reconstruction which only calculates x-coordinate and y-coordinate TV to transform CT images into sparse domain, we propose a multi-directional TV to transform tomographic image into sparse domain for low-dose reconstruction. Our method considers all possible directions of TV calculations around a pixel, so the sparse transform for CS based reconstruction is more accurate. In 2D CT reconstruction, we use eight-directional TV to transform CT image into sparse domain. Furthermore, we also use 26-directional TV for 3D reconstruction. This multi-directional sparse transform method makes CS based reconstruction algorithm more powerful to reduce noise and increase image quality. To validate and evaluate the performance of this multi-directional sparse transform method, we use both Shepp-Logan phantom and a head phantom as the targets for reconstruction with the corresponding simulated sparse projection data (angular sampling interval is 5 deg and 6 deg, respectively). From the results, the multi-directional TV method can reconstruct images with relatively less artifacts compared with traditional CS based reconstruction algorithm which only calculates x-coordinate and y-coordinate TV. We also choose RMSE, PSNR, UQI to be the parameters for quantitative analysis. From the results of quantitative analysis, no matter which parameter is calculated, the multi-directional TV method, which we proposed, is better. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compressed%20sensing%20%28CS%29" title="compressed sensing (CS)">compressed sensing (CS)</a>, <a href="https://publications.waset.org/abstracts/search?q=low-dose%20CT%20reconstruction" title=" low-dose CT reconstruction"> low-dose CT reconstruction</a>, <a href="https://publications.waset.org/abstracts/search?q=total%20variation%20%28TV%29" title=" total variation (TV)"> total variation (TV)</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-directional%20gradient%20operator" title=" multi-directional gradient operator"> multi-directional gradient operator</a> </p> <a href="https://publications.waset.org/abstracts/77716/development-of-a-few-view-computed-tomographic-reconstruction-algorithm-using-multi-directional-total-variation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77716.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">256</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">608</span> KSVD-SVM Approach for Spontaneous Facial Expression Recognition</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dawood%20Al%20Chanti">Dawood Al Chanti</a>, <a href="https://publications.waset.org/abstracts/search?q=Alice%20Caplier"> Alice Caplier</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Sparse representations of signals have received a great deal of attention in recent years. In this paper, the interest of using sparse representation as a mean for performing sparse discriminative analysis between spontaneous facial expressions is demonstrated. An automatic facial expressions recognition system is presented. It uses a KSVD-SVM approach which is made of three main stages: A pre-processing and feature extraction stage, which solves the problem of shared subspace distribution based on the random projection theory, to obtain low dimensional discriminative and reconstructive features; A dictionary learning and sparse coding stage, which uses the KSVD model to learn discriminative under or over dictionaries for sparse coding; Finally a classification stage, which uses a SVM classifier for facial expressions recognition. Our main concern is to be able to recognize non-basic affective states and non-acted expressions. Extensive experiments on the JAFFE static acted facial expressions database but also on the DynEmo dynamic spontaneous facial expressions database exhibit very good recognition rates. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dictionary%20learning" title="dictionary learning">dictionary learning</a>, <a href="https://publications.waset.org/abstracts/search?q=random%20projection" title=" random projection"> random projection</a>, <a href="https://publications.waset.org/abstracts/search?q=pose%20and%20spontaneous%20facial%20expression" title=" pose and spontaneous facial expression"> pose and spontaneous facial expression</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse%20representation" title=" sparse representation"> sparse representation</a> </p> <a href="https://publications.waset.org/abstracts/51683/ksvd-svm-approach-for-spontaneous-facial-expression-recognition" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51683.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">305</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">607</span> Existence and Construction of Maximal Rectangular Duals</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Krishnendra%20Shekhawat">Krishnendra Shekhawat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Given a graph G = (V, E), a rectangular dual of G represents the vertices of G by a set of interior-disjoint rectangles such that two rectangles touch if and only if there is an edge between the two corresponding vertices in G. Rectangular duals do not exist for every graph, so we can define maximal rectangular duals. A maximal rectangular dual is a rectangular dual of a graph G such that there exists no graph G ′ with a rectangular dual where G is a subgraph of G ′. In this paper, we enumerate all maximal rectangular duals (or, to be precise, the corresponding planar graphs) up to six nodes and presents a necessary condition for the existence of a rectangular dual. This work allegedly has applications in integrated circuit design and architectural floor plans. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adjacency" title="adjacency">adjacency</a>, <a href="https://publications.waset.org/abstracts/search?q=degree%20sequence" title=" degree sequence"> degree sequence</a>, <a href="https://publications.waset.org/abstracts/search?q=dual%20graph" title=" dual graph"> dual graph</a>, <a href="https://publications.waset.org/abstracts/search?q=rectangular%20dual" title=" rectangular dual"> rectangular dual</a> </p> <a href="https://publications.waset.org/abstracts/62583/existence-and-construction-of-maximal-rectangular-duals" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/62583.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">266</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">606</span> Characterising Stable Model by Extended Labelled Dependency Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Asraful%20Islam">Asraful Islam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Extended dependency graph (EDG) is a state-of-the-art isomorphic graph to represent normal logic programs (NLPs) that can characterize the consistency of NLPs by graph analysis. To construct the vertices and arcs of an EDG, additional renaming atoms and rules besides those the given program provides are used, resulting in higher space complexity compared to the corresponding traditional dependency graph (TDG). In this article, we propose an extended labeled dependency graph (ELDG) to represent an NLP that shares an equal number of nodes and arcs with TDG and prove that it is isomorphic to the domain program. The number of nodes and arcs used in the underlying dependency graphs are formulated to compare the space complexity. Results show that ELDG uses less memory to store nodes, arcs, and cycles compared to EDG. To exhibit the desirability of ELDG, firstly, the stable models of the kernel form of NLP are characterized by the admissible coloring of ELDG; secondly, a relation of the stable models of a kernel program with the handles of the minimal, odd cycles appearing in the corresponding ELDG has been established; thirdly, to our best knowledge, for the first time an inverse transformation from a dependency graph to the representing NLP w.r.t. ELDG has been defined that enables transferring analytical results from the graph to the program straightforwardly. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=normal%20logic%20program" title="normal logic program">normal logic program</a>, <a href="https://publications.waset.org/abstracts/search?q=isomorphism%20of%20graph" title=" isomorphism of graph"> isomorphism of graph</a>, <a href="https://publications.waset.org/abstracts/search?q=extended%20labelled%20dependency%20graph" title=" extended labelled dependency graph"> extended labelled dependency graph</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20graph%20transforma-tion" title=" inverse graph transforma-tion"> inverse graph transforma-tion</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20colouring" title=" graph colouring"> graph colouring</a> </p> <a href="https://publications.waset.org/abstracts/137606/characterising-stable-model-by-extended-labelled-dependency-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/137606.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">213</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">605</span> Sparse-View CT Reconstruction Based on Nonconvex L1 − L2 Regularizations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Pour%20Yazdanpanah">Ali Pour Yazdanpanah</a>, <a href="https://publications.waset.org/abstracts/search?q=Farideh%20Foroozandeh%20Shahraki"> Farideh Foroozandeh Shahraki</a>, <a href="https://publications.waset.org/abstracts/search?q=Emma%20Regentova"> Emma Regentova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The reconstruction from sparse-view projections is one of important problems in computed tomography (CT) limited by the availability or feasibility of obtaining of a large number of projections. Traditionally, convex regularizers have been exploited to improve the reconstruction quality in sparse-view CT, and the convex constraint in those problems leads to an easy optimization process. However, convex regularizers often result in a biased approximation and inaccurate reconstruction in CT problems. Here, we present a nonconvex, Lipschitz continuous and non-smooth regularization model. The CT reconstruction is formulated as a nonconvex constrained L1 − L2 minimization problem and solved through a difference of convex algorithm and alternating direction of multiplier method which generates a better result than L0 or L1 regularizers in the CT reconstruction. We compare our method with previously reported high performance methods which use convex regularizers such as TV, wavelet, curvelet, and curvelet+TV (CTV) on the test phantom images. The results show that there are benefits in using the nonconvex regularizer in the sparse-view CT reconstruction. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=computed%20tomography" title="computed tomography">computed tomography</a>, <a href="https://publications.waset.org/abstracts/search?q=non-convex" title=" non-convex"> non-convex</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse-view%20reconstruction" title=" sparse-view reconstruction"> sparse-view reconstruction</a>, <a href="https://publications.waset.org/abstracts/search?q=L1-L2%20minimization" title=" L1-L2 minimization"> L1-L2 minimization</a>, <a href="https://publications.waset.org/abstracts/search?q=difference%20of%20convex%20functions" title=" difference of convex functions"> difference of convex functions</a> </p> <a href="https://publications.waset.org/abstracts/70473/sparse-view-ct-reconstruction-based-on-nonconvex-l1-l2-regularizations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/70473.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">316</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">604</span> Introduction to Paired Domination Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Puttaswamy">Puttaswamy</a>, <a href="https://publications.waset.org/abstracts/search?q=Anwar%20Alwardi"> Anwar Alwardi</a>, <a href="https://publications.waset.org/abstracts/search?q=Nayaka%20S.%20R."> Nayaka S. R.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=domination%20polynomial" title="domination polynomial">domination polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20dominating%20set" title=" paired dominating set"> paired dominating set</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20domination%20number" title=" paired domination number"> paired domination number</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20domination%20polynomial" title=" paired domination polynomial"> paired domination polynomial</a> </p> <a href="https://publications.waset.org/abstracts/52964/introduction-to-paired-domination-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52964.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">232</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">603</span> A New Framework for ECG Signal Modeling and Compression Based on Compressed Sensing Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Siavash%20Eftekharifar">Siavash Eftekharifar</a>, <a href="https://publications.waset.org/abstracts/search?q=Tohid%20Yousefi%20Rezaii"> Tohid Yousefi Rezaii</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahdi%20Shamsi"> Mahdi Shamsi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of this paper is to exploit compressed sensing (CS) method in order to model and compress the electrocardiogram (ECG) signals at a high compression ratio. In order to obtain a sparse representation of the ECG signals, first a suitable basis matrix with Gaussian kernels, which are shown to nicely fit the ECG signals, is constructed. Then the sparse model is extracted by applying some optimization technique. Finally, the CS theory is utilized to obtain a compressed version of the sparse signal. Reconstruction of the ECG signal from the compressed version is also done to prove the reliability of the algorithm. At this stage, a greedy optimization technique is used to reconstruct the ECG signal and the Mean Square Error (MSE) is calculated to evaluate the precision of the proposed compression method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compressed%20sensing" title="compressed sensing">compressed sensing</a>, <a href="https://publications.waset.org/abstracts/search?q=ECG%20compression" title=" ECG compression"> ECG compression</a>, <a href="https://publications.waset.org/abstracts/search?q=Gaussian%20kernel" title=" Gaussian kernel"> Gaussian kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse%20representation" title=" sparse representation"> sparse representation</a> </p> <a href="https://publications.waset.org/abstracts/31469/a-new-framework-for-ecg-signal-modeling-and-compression-based-on-compressed-sensing-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31469.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">462</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">602</span> Eccentric Connectivity Index, First and Second Zagreb Indices of Corona Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Kulandai%20Therese">A. Kulandai Therese</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics.In this paper, we present the explicit eccentric connectivity index, first and second Zagreb indices for a Corona graph and sub division-related corona graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=corona%20graph" title="corona graph">corona graph</a>, <a href="https://publications.waset.org/abstracts/search?q=degree" title=" degree"> degree</a>, <a href="https://publications.waset.org/abstracts/search?q=eccentricity" title=" eccentricity"> eccentricity</a>, <a href="https://publications.waset.org/abstracts/search?q=eccentric%20connectivity%20index" title=" eccentric connectivity index"> eccentric connectivity index</a>, <a href="https://publications.waset.org/abstracts/search?q=first%20zagreb%20index" title=" first zagreb index"> first zagreb index</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20zagreb%20index" title=" second zagreb index"> second zagreb index</a>, <a href="https://publications.waset.org/abstracts/search?q=subdivision%20graphs" title=" subdivision graphs"> subdivision graphs</a> </p> <a href="https://publications.waset.org/abstracts/16768/eccentric-connectivity-index-first-and-second-zagreb-indices-of-corona-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16768.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">338</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">601</span> 2D Structured Non-Cyclic Fuzzy Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=T.%20Pathinathan">T. Pathinathan</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Peter"> M. Peter</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=double%20layered%20fuzzy%20graph" title="double layered fuzzy graph">double layered fuzzy graph</a>, <a href="https://publications.waset.org/abstracts/search?q=double%20layered%20non%E2%80%93cyclic%20fuzzy%20graph" title=" double layered non–cyclic fuzzy graph"> double layered non–cyclic fuzzy graph</a>, <a href="https://publications.waset.org/abstracts/search?q=order" title=" order"> order</a>, <a href="https://publications.waset.org/abstracts/search?q=degree%20and%20size" title=" degree and size"> degree and size</a> </p> <a href="https://publications.waset.org/abstracts/80562/2d-structured-non-cyclic-fuzzy-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80562.pdf" target="_blank" class="btn btn-primary 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