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

2015
*
arXiv
*
pre-print

The crux of our

arXiv:1406.4173v2
fatcat:o6oqa5zwffd5jaatl4nivtn4je
*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 ...##
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A Divide-and-Conquer Algorithm for Betweenness Centrality
[chapter]

2015
*
Proceedings of the 2015 SIAM International Conference on Data Mining
*

Given

doi:10.1137/1.9781611974010.49
dblp:conf/sdm/ErdosIBT15
fatcat:lp55mhxtmzc3jmfxxnpgh5akji
*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. ...##
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Utility-Based Graph Summarization: New and Improved
[article]

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

arXiv:2006.08949v1
fatcat:poqdbqwwwbgkjc2o34dozqcqgq
*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*. ...##
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Greedy Algorithms for Steiner Forest
[article]

2014
*
arXiv
*
pre-print

We consider the following greedy

arXiv:1412.7693v1
fatcat:2wkibja5fvau7gvqlfo3pq2jhi
*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. ...##
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Partitioning graphs to speed up point-to-point shortest path computations

2011
*
IEEE Conference on Decision and Control and European Control Conference
*

Computing the

doi:10.1109/cdc.2011.6160321
dblp:conf/cdc/SongW11
fatcat:24lqap4s7fb3nlftum4txdbete
*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). ...##
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Privacy Preservation by k-Anonymization of Weighted Social Networks

2012
*
2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
*

Privacy preserving analysis of

doi:10.1109/asonam.2012.75
dblp:conf/asunam/SkarkalaMGMTM12
fatcat:yqal6zswmre43ciqdgr6v6mbae
*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. ...##
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Keyword search on external memory data graphs

2008
*
Proceedings of the VLDB Endowment
*

We propose

doi:10.14778/1453856.1453982
fatcat:u4xn6hqyrfayvotw3tsqui6coy
*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. ...##
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MATria: a unified centrality algorithm

2019
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BMC Bioinformatics
*

Results: We instead generalize the results of any k centrality

doi:10.1186/s12859-019-2820-7
fatcat:vdulut75n5fkvbtwox4rj5oixe
*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. ...##
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MATria: A unified centrality algorithm

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

doi:10.1109/iccabs.2017.8114289
dblp:conf/iccabs/CickovskiAN17
fatcat:i3fj5oypizblvbj7mbact4cthi
*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. ...##
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When trees collide

1991
*
Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91
*

An instance consists of

doi:10.1145/103418.103437
dblp:conf/stoc/AgrawalKR91
fatcat:je4bopd2vfbkpcbivmjinad7oy
*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. ...##
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When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks

1995
*
SIAM journal on computing (Print)
*

An instance consists of

doi:10.1137/s0097539792236237
fatcat:hmehrhjj6nfjlnvj35ypnh3hde
*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. ...##
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Cops, Robbers, and Threatening Skeletons: Padded Decomposition for Minor-Free Graphs
[article]

2021
*
arXiv
*
pre-print

Our result is obtained by

arXiv:1311.3048v2
fatcat:xwccz73ionhgtahdjiksslah2m
*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. ...##
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Cops, robbers, and threatening skeletons

2014
*
Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14
*

Our result is obtained by

doi:10.1145/2591796.2591849
dblp:conf/stoc/AbrahamGGNT14
fatcat:vfytrjf7h5aabht3fbdtvuxoj4
*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. ...##
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An approximation algorithm for shortest path based on the hierarchy networks
[article]

2015
*
arXiv
*
pre-print

It is

arXiv:1405.4051v2
fatcat:2er3veanajf4rffnn4k4wylaia
*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. ...##
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Utility-driven graph summarization

2018
*
Proceedings of the VLDB Endowment
*

speed-up for graph

doi:10.14778/3297753.3297755
fatcat:5oqosozrkfa2hgzqq3iwgeqfae
*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 ...
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