The Experts below are selected from a list of 72 Experts worldwide ranked by ideXlab platform
Arunabha Sen - One of the best experts on this subject based on the ideXlab platform.
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relay node placement under budget constraint
Pervasive and Mobile Computing, 2019Co-Authors: Chenyang Zhou, Anisha Mazumder, Arun Das, Kaustav Basu, Navid Matinmoghaddam, Saharnaz Mehrani, Arunabha SenAbstract:Abstract The relay node placement problem in the wireless sensor network domain has been studied extensively. But under a fixed budget, it may be impossible to procure the minimum number of relay nodes needed to design a connected network of sensor and relay nodes. Nevertheless, one would still like to design a network with high level of connectedness, or low Disconnectedness. In this paper, we introduce the notion of a measure of the “connectedness” of a Disconnected Graph. We study a family of problems whose goal is to design a network with “maximal connectedness” subject to a fixed budget constraint.
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relay node placement under budget constraint
International Conference of Distributed Computing and Networking, 2018Co-Authors: Chenyang Zhou, Anisha Mazumder, Arun Das, Kaustav Basu, Navid Matinmoghaddam, Saharnaz Mehrani, Arunabha SenAbstract:The relay node placement problem in the wireless sensor network domain has been studied extensively over the past few years. The objective of most of these problems, is to place the fewest number of relay nodes in the deployment area so that the network, formed by the sensor and the relay nodes, is connected. Under the fixed budget scenario, the expense involved in procuring the minimum number of relay nodes to make the network connected, may exceed the budget. Although, in this case, one must give up the idea of having of a connected network but one would still like to design a network with a high level of connectedness, or a low level of Disconnectedness. In this paper, we introduce the notion of disconnectivity, a measure of the "connectedness" of a Disconnected Graph. We study a family of problems whose goal is to design a network with "maximal connectedness" or "minimal Disconnectedness", subject to a fixed budget constraint. We show that all problems in this family are NP-Complete and present an approximation algorithm with a performance bound of 1/10 for the problem that maximizes the size of the largest connected components, and inapproximability results for the problem that maximizes the size of the smallest connected component and the problem that minimizes the number of connected components. In addition, we present future direction of our research on this topic.
Lawrence Carin - One of the best experts on this subject based on the ideXlab platform.
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scalable gromov wasserstein learning for Graph partitioning and matching
arXiv: Learning, 2019Co-Authors: Dixin Luo, Lawrence CarinAbstract:We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale Graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on Graphs. Given two Graphs, the optimal transport associated with their Gromov-Wasserstein discrepancy provides the correspondence between their nodes and achieves Graph matching. When one of the Graphs has isolated but self-connected nodes ($i.e.$, a Disconnected Graph), the optimal transport indicates the clustering structure of the other Graph and achieves Graph partitioning. Using this concept, we extend our method to multi-Graph partitioning and matching by learning a Gromov-Wasserstein barycenter Graph for multiple observed Graphs; the barycenter Graph plays the role of the Disconnected Graph, and since it is learned, so is the clustering. Our method combines a recursive $K$-partition mechanism with a regularized proximal gradient algorithm, whose time complexity is $\mathcal{O}(K(E+V)\log_K V)$ for Graphs with $V$ nodes and $E$ edges. To our knowledge, our method is the first attempt to make Gromov-Wasserstein discrepancy applicable to large-scale Graph analysis and unify Graph partitioning and matching into the same framework. It outperforms state-of-the-art Graph partitioning and matching methods, achieving a trade-off between accuracy and efficiency.
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scalable gromov wasserstein learning for Graph partitioning and matching
Neural Information Processing Systems, 2019Co-Authors: Dixin Luo, Lawrence CarinAbstract:We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale Graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on Graphs. Given two Graphs, the optimal transport associated with their Gromov-Wasserstein discrepancy provides the correspondence between their nodes and achieves Graph matching. When one of the Graphs is a predefined Graph with isolated but self-connected nodes ($i.e.$, Disconnected Graph), the optimal transport indicates the clustering structure of the other Graph and achieves Graph partitioning. Further, we extend our method to multi-Graph partitioning and matching by learning a Gromov-Wasserstein barycenter Graph for multiple observed Graphs. Our method combines a recursive $K$-partition mechanism with a warm-start proximal gradient algorithm, whose time complexity is $\mathcal{O}(K(E+V)\log_K V)$ for Graphs with $V$ nodes and $E$ edges. To our knowledge, our method is the first attempt to make Gromov-Wasserstein discrepancy applicable to large-scale Graph analysis and unify Graph partitioning and matching into the same framework. It outperforms state-of-the-art Graph partitioning and matching methods, achieving a trade-off between accuracy and efficiency.
Gunes Ercal - One of the best experts on this subject based on the ideXlab platform.
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on the cover time and mixing time of random geometric Graphs
Theoretical Computer Science, 2007Co-Authors: Chen Avin, Gunes ErcalAbstract:The cover time and mixing time of Graphs has much relevance to algorithmic applications and has been extensively investigated. Recently, with the advent of ad hoc and sensor networks, an interesting class of random Graphs, namely random geometric Graphs, has gained new relevance and its properties have been the subject of much study. A random geometric Graph G(n,r) is obtained by placing n points uniformly at random on the unit square and connecting two points iff their Euclidean distance is at most r. The phase transition behavior with respect to the radius r of such Graphs has been of special interest. We show that there exists a critical radius r"o"p"t such that for any r>=r"o"p"tG(n,r) has optimal cover time of @Q(nlogn) with high probability, and, importantly, r"o"p"[email protected](r"c"o"n) where r"c"o"n denotes the critical radius guaranteeing asymptotic connectivity. Moreover, since a Disconnected Graph has infinite cover time, there is a phase transition and the corresponding threshold width is O(r"c"o"n). On the other hand, the radius required for rapid mixing r"r"a"p"i"[email protected](r"c"o"n), and, in particular, r"r"a"p"i"[email protected](1/poly(logn)). We are able to draw our results by giving a tight bound on the electrical resistance and conductance of G(n,r) via certain constructed flows.
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on the cover time and mixing time of random geometric Graphs
International Colloquium on Automata Languages and Programming, 2007Co-Authors: Chen Avin, Gunes ErcalAbstract:The cover time and mixing time of Graphs has much relevance to algorithmic applications and has been extensively investigated. Recently, with the advent of ad hoc and sensor networks, an interesting class of random Graphs, namely random geometric Graphs, has gained new relevance and its properties have been the subject of much study. A random geometric Graph G(n, r) is obtained by placing n points uniformly at random on the unit square and connecting two points iff their Euclidean distance is at most r. The phase transition behavior with respect to the radius r of such Graphs has been of special interest. We show that there exists a critical radius r opt such that for any r ≥ r opt G(n, r) has optimal cover time of Θ(n log n) with high probability, and, importantly, r opt = Θ(r con ) where r con denotes the critical radius guaranteeing asymptotic connectivity. Moreover, since a Disconnected Graph has infinite cover time, there is a phase transition and the corresponding threshold width is O(r con ). On the other hand, the radius required for rapid mixing r rapid = ω(r con ), and, in particular, r rapid = Θ(1/poly(log n)). We are able to draw our results by giving a tight bound on the electrical resistance and conductance of G(n, r) via certain constructed flows.
Chenyang Zhou - One of the best experts on this subject based on the ideXlab platform.
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relay node placement under budget constraint
Pervasive and Mobile Computing, 2019Co-Authors: Chenyang Zhou, Anisha Mazumder, Arun Das, Kaustav Basu, Navid Matinmoghaddam, Saharnaz Mehrani, Arunabha SenAbstract:Abstract The relay node placement problem in the wireless sensor network domain has been studied extensively. But under a fixed budget, it may be impossible to procure the minimum number of relay nodes needed to design a connected network of sensor and relay nodes. Nevertheless, one would still like to design a network with high level of connectedness, or low Disconnectedness. In this paper, we introduce the notion of a measure of the “connectedness” of a Disconnected Graph. We study a family of problems whose goal is to design a network with “maximal connectedness” subject to a fixed budget constraint.
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relay node placement under budget constraint
International Conference of Distributed Computing and Networking, 2018Co-Authors: Chenyang Zhou, Anisha Mazumder, Arun Das, Kaustav Basu, Navid Matinmoghaddam, Saharnaz Mehrani, Arunabha SenAbstract:The relay node placement problem in the wireless sensor network domain has been studied extensively over the past few years. The objective of most of these problems, is to place the fewest number of relay nodes in the deployment area so that the network, formed by the sensor and the relay nodes, is connected. Under the fixed budget scenario, the expense involved in procuring the minimum number of relay nodes to make the network connected, may exceed the budget. Although, in this case, one must give up the idea of having of a connected network but one would still like to design a network with a high level of connectedness, or a low level of Disconnectedness. In this paper, we introduce the notion of disconnectivity, a measure of the "connectedness" of a Disconnected Graph. We study a family of problems whose goal is to design a network with "maximal connectedness" or "minimal Disconnectedness", subject to a fixed budget constraint. We show that all problems in this family are NP-Complete and present an approximation algorithm with a performance bound of 1/10 for the problem that maximizes the size of the largest connected components, and inapproximability results for the problem that maximizes the size of the smallest connected component and the problem that minimizes the number of connected components. In addition, we present future direction of our research on this topic.
Dixin Luo - One of the best experts on this subject based on the ideXlab platform.
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scalable gromov wasserstein learning for Graph partitioning and matching
arXiv: Learning, 2019Co-Authors: Dixin Luo, Lawrence CarinAbstract:We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale Graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on Graphs. Given two Graphs, the optimal transport associated with their Gromov-Wasserstein discrepancy provides the correspondence between their nodes and achieves Graph matching. When one of the Graphs has isolated but self-connected nodes ($i.e.$, a Disconnected Graph), the optimal transport indicates the clustering structure of the other Graph and achieves Graph partitioning. Using this concept, we extend our method to multi-Graph partitioning and matching by learning a Gromov-Wasserstein barycenter Graph for multiple observed Graphs; the barycenter Graph plays the role of the Disconnected Graph, and since it is learned, so is the clustering. Our method combines a recursive $K$-partition mechanism with a regularized proximal gradient algorithm, whose time complexity is $\mathcal{O}(K(E+V)\log_K V)$ for Graphs with $V$ nodes and $E$ edges. To our knowledge, our method is the first attempt to make Gromov-Wasserstein discrepancy applicable to large-scale Graph analysis and unify Graph partitioning and matching into the same framework. It outperforms state-of-the-art Graph partitioning and matching methods, achieving a trade-off between accuracy and efficiency.
-
scalable gromov wasserstein learning for Graph partitioning and matching
Neural Information Processing Systems, 2019Co-Authors: Dixin Luo, Lawrence CarinAbstract:We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale Graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on Graphs. Given two Graphs, the optimal transport associated with their Gromov-Wasserstein discrepancy provides the correspondence between their nodes and achieves Graph matching. When one of the Graphs is a predefined Graph with isolated but self-connected nodes ($i.e.$, Disconnected Graph), the optimal transport indicates the clustering structure of the other Graph and achieves Graph partitioning. Further, we extend our method to multi-Graph partitioning and matching by learning a Gromov-Wasserstein barycenter Graph for multiple observed Graphs. Our method combines a recursive $K$-partition mechanism with a warm-start proximal gradient algorithm, whose time complexity is $\mathcal{O}(K(E+V)\log_K V)$ for Graphs with $V$ nodes and $E$ edges. To our knowledge, our method is the first attempt to make Gromov-Wasserstein discrepancy applicable to large-scale Graph analysis and unify Graph partitioning and matching into the same framework. It outperforms state-of-the-art Graph partitioning and matching methods, achieving a trade-off between accuracy and efficiency.