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A Divide-and-Conquer Algorithm for Betweenness Centrality [article]

Dora Erdos, Vatche Ishakian, Azer Bestavros, Evimaria Terzi
2015 arXiv   pre-print
The crux of our algorithm is that we create a sketch of the graph, that we call the skeleton, by replacing subgraphs with simpler graph structures.  ...  To date, the best known exact and centralized algorithm for this task is an algorithm proposed in 2001 by Brandes.  ...  The idea is to iterate over all pairs of supernodes G i and G j and compute the centrality C ij (v) of nodes when we only consider shortest paths that have a node in G i as their source and a node in G  ... 
arXiv:1406.4173v2 fatcat:o6oqa5zwffd5jaatl4nivtn4je

A Divide-and-Conquer Algorithm for Betweenness Centrality [chapter]

Dóra Erdős, Vatche Ishakian, Azer Bestavros, Evimaria Terzi
2015 Proceedings of the 2015 SIAM International Conference on Data Mining  
Given a set of target nodes S in a graph G we define the betweenness centrality of a node v with respect to S as the fraction of shortest paths among nodes in S that contain v.  ...  For this setting we describe Brandes++, a divide-and-conquer algorithm that can efficiently compute the exact values of betweenness scores.  ...  The edges E sk serve the purpose of representing the possible shortest paths between pairs of frontier nodes, and as a result, the paths between pairs of target nodes in G.  ... 
doi:10.1137/1.9781611974010.49 dblp:conf/sdm/ErdosIBT15 fatcat:lp55mhxtmzc3jmfxxnpgh5akji

Utility-Based Graph Summarization: New and Improved [article]

Mahdi Hajiabadi, Jasbir Singh, Venkatesh Srinivasan, Alex Thomo
2020 arXiv   pre-print
Third, we show that our graph summaries can be used as-is to answer several important classes of queries, such as triangle enumeration, Pagerank, and shortest paths.  ...  Our algorithm achieves this by combining a memory reduction technique and a novel binary-search approach.  ...  Otherwise, as nodes in a supernode have the same connectivity, it can be seen that that path is not the shortest.  ... 
arXiv:2006.08949v1 fatcat:poqdbqwwwbgkjc2o34dozqcqgq

Greedy Algorithms for Steiner Forest [article]

Anupam Gupta, Amit Kumar
2014 arXiv   pre-print
We consider the following greedy algorithm: Given terminal pairs in a metric space, call a terminal "active" if its distance to its partner is non-zero.  ...  Pick the two closest active terminals (say s_i, t_j), set the distance between them to zero, and buy a path connecting them. Recompute the metric, and repeat.  ...  Ravi for suggesting the problem to us, for many discussions about it over the years, and for the algorithm name. We also thank Chandra Chekuri, Jochen Könemann, Stefano Leonardi, and Tim Roughgarden.  ... 
arXiv:1412.7693v1 fatcat:2wkibja5fvau7gvqlfo3pq2jhi

Partitioning graphs to speed up point-to-point shortest path computations

Qing Song, Xiaofan Wang
2011 IEEE Conference on Decision and Control and European Control Conference  
Computing the shortest paths in graphs is a fundamental problem with numerous applications.  ...  The rapid growth of network in size and complexity has made it necessary to decrease the execution time of the shortest path algorithm.  ...  The algorithm first grows a shortest path tree over G A , starting from the destination supernode G t (which contains the destination node t).  ... 
doi:10.1109/cdc.2011.6160321 dblp:conf/cdc/SongW11 fatcat:24lqap4s7fb3nlftum4txdbete

Privacy Preservation by k-Anonymization of Weighted Social Networks

M. E. Skarkala, M. Maragoudakis, S. Gritzalis, L. Mitrou, H. Toivonen, P. Moen
2012 2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining  
Privacy preserving analysis of a social network aims at a better understanding of the network and its behavior, while at the same time protecting the privacy of its individuals.  ...  We propose a method that provides k-anonymity of nodes against attacks where the adversary has information about the structure of the network, including its edge weights.  ...  ACKNOWLEDGEMENTS This work has been supported by the Algorithmic Data Analysis (Algodan) Center of Excellence of the Academy of Finland.  ... 
doi:10.1109/asonam.2012.75 dblp:conf/asunam/SkarkalaMGMTM12 fatcat:yqal6zswmre43ciqdgr6v6mbae

Keyword search on external memory data graphs

Bhavana Bharat Dalvi, Meghana Kshirsagar, S. Sudarshan
2008 Proceedings of the VLDB Endowment  
We propose a graph representation technique that combines a condensed version of the graph (the "supernode graph") which is always memory resident, along with whatever parts of the detailed graph are in  ...  We compare our algorithms with a virtual memory approach on several real data sets. Our experimental results show significant benefits in terms of reduction in IO due to our algorithms.  ...  are removed from all shortest path iterators where the supernode is present.  ... 
doi:10.14778/1453856.1453982 fatcat:u4xn6hqyrfayvotw3tsqui6coy

MATria: a unified centrality algorithm

Trevor Cickovski, Vanessa Aguiar-Pulido, Giri Narasimhan
2019 BMC Bioinformatics  
Results: We instead generalize the results of any k centrality algorithms through our iterative algorithm MATRIA, producing a single ranked and unified set of central nodes.  ...  Conclusions: Our results show iteration to be a powerful technique that can eliminate spatial bias among central nodes, increasing the level of agreement between algorithms with various importance definitions  ...  All applicable input data is also available, along with sample executions from this paper at http://biorg.cs.fiu. edu/pluma/matria.  ... 
doi:10.1186/s12859-019-2820-7 fatcat:vdulut75n5fkvbtwox4rj5oixe

MATria: A unified centrality algorithm

Trevor Cickovski, Vanessa Aguiar-Pulido, Giri Narasimhan
2017 2017 IEEE 7th International Conference on Computational Advances in Bio and Medical Sciences (ICCABS)  
Results: We instead generalize the results of any k centrality algorithms through our iterative algorithm MATRIA, producing a single ranked and unified set of central nodes.  ...  Conclusions: Our results show iteration to be a powerful technique that can eliminate spatial bias among central nodes, increasing the level of agreement between algorithms with various importance definitions  ...  All applicable input data is also available, along with sample executions from this paper at http://biorg.cs.fiu. edu/pluma/matria.  ... 
doi:10.1109/iccabs.2017.8114289 dblp:conf/iccabs/CickovskiAN17 fatcat:i3fj5oypizblvbj7mbact4cthi

When trees collide

Ajit Agrawal, Philip Klein, R. Ravi
1991 Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91  
An instance consists of a network with link-costs and} for each pair {i, j} of nodes, an edge-connectivity requirement Tij.  ...  As a consequence of the proof of this theorem, we obtain an approximation algorithm for optimally packing these cuts; we show that this algorithm has application to estimating the reliability of a probabilistic  ...  case, except that Dijkstra's shortest-path algorithm is used in place of breadth-first search.  ... 
doi:10.1145/103418.103437 dblp:conf/stoc/AgrawalKR91 fatcat:je4bopd2vfbkpcbivmjinad7oy

When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks

Ajit Agrawal, Philip Klein, R. Ravi
1995 SIAM journal on computing (Print)  
An instance consists of a network with link-costs and} for each pair {i, j} of nodes, an edge-connectivity requirement Tij.  ...  As a consequence of the proof of this theorem, we obtain an approximation algorithm for optimally packing these cuts; we show that this algorithm has application to estimating the reliability of a probabilistic  ...  case, except that Dijkstra's shortest-path algorithm is used in place of breadth-first search.  ... 
doi:10.1137/s0097539792236237 fatcat:hmehrhjj6nfjlnvj35ypnh3hde

Cops, Robbers, and Threatening Skeletons: Padded Decomposition for Minor-Free Graphs [article]

Ittai Abraham and Cyril Gavoille and Anupam Gupta and Ofer Neiman and Kunal Talwar
2021 arXiv   pre-print
Our result is obtained by a new approach to relate the topological properties (excluding a minor) of a graph to its geometric properties (the induced shortest path metric).  ...  We prove that any graph excluding K_r as a minor has can be partitioned into clusters of diameter at most Δ while removing at most O(r/Δ) fraction of the edges.  ...  A. Gupta and C. Gavoille thank Microsoft Research SVC for their kind hospitality. We also thank Arnold Filtser for pointing out an error in the original proof of Lemma 7.  ... 
arXiv:1311.3048v2 fatcat:xwccz73ionhgtahdjiksslah2m

Cops, robbers, and threatening skeletons

Ittai Abraham, Cyril Gavoille, Anupam Gupta, Ofer Neiman, Kunal Talwar
2014 Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14  
Our result is obtained by a new approach to relate the topological properties (excluding a minor) of a graph to its geometric properties (the induced shortest path metric).  ...  We prove that any graph excluding K r as a minor has can be partitioned into clusters of diameter at most ∆ while removing at most O(r/∆) fraction of the edges.  ...  A. Gupta thanks Microsoft Research SVC for their kind hospitality.  ... 
doi:10.1145/2591796.2591849 dblp:conf/stoc/AbrahamGGNT14 fatcat:vfytrjf7h5aabht3fbdtvuxoj4

An approximation algorithm for shortest path based on the hierarchy networks [article]

Shi-nan Gong, Duan-bing Chen, Hui Gao, Guan-nan Wang, Liang-wei Wang
2015 arXiv   pre-print
It is a critical issue to compute the shortest paths between nodes in networks.  ...  Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity.  ...  Algorithm 3 requires at most O(kn 2 ) time to compute the shortest paths for all pair of nodes.  ... 
arXiv:1405.4051v2 fatcat:2er3veanajf4rffnn4k4wylaia

Utility-driven graph summarization

K. Ashwin Kumar, Petros Efstathopoulos
2018 Proceedings of the VLDB Endowment  
speed-up for graph algorithms, 2) graph storage space reduction, 3) faster network transmission, 4) improved data privacy, 5) more effective graph visualization, etc.  ...  This enables a user to query a graph summary that is conditioned on a user-specified utility value. We present both exhaustive and scalable approaches for implementing our proposed solution.  ...  The most common betweenness centrality metric is based on shortest paths, where the centrality of an edge e is essentially an average number of shortest paths connecting all pairs of nodes in the graph  ... 
doi:10.14778/3297753.3297755 fatcat:5oqosozrkfa2hgzqq3iwgeqfae
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