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Improving the betweenness centrality of a node by adding links [article]

Elisabetta Bergamini, Pierluigi Crescenzi, Gianlorenzo D'Angelo, Henning Meyerhenke, Lorenzo Severini, Yllka Velaj
2018 arXiv   pre-print
Betweenness is a well-known centrality measure that ranks the nodes according to their participation in the shortest paths of a network.  ...  Using the dynamic algorithm, we are now able to compute an approximation of MBI on networks with up to 10^5 edges in most cases in a matter of seconds or a few minutes.  ...  preceding v in the shortest paths from s to v, for all node pairs (s, v).  ... 
arXiv:1702.05284v2 fatcat:s5nzx3jicvg73fcz5dbgtrtzl4

A Survey of Shortest-Path Algorithms [article]

Amgad Madkour, Walid G. Aref, Faizan Ur Rehman, Mohamed Abdur Rahman, Saleh Basalamah
2017 arXiv   pre-print
Other important dimensions of the taxonomy include whether the shortest-path algorithm operates over a static or a dynamic graph, whether the shortest-path algorithm produces exact or approximate answers  ...  A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph.  ...  Aref's research has been supported in part by the National Science Foundation under Grant IIS 1117766.  ... 
arXiv:1705.02044v1 fatcat:fkh55mi34vezhbvjbzu7ekmdai

On Dynamic Shortest Paths Problems [chapter]

Liam Roditty, Uri Zwick
2004 Lecture Notes in Computer Science  
directed or undirected graphs, are, in a strong sense, at least as hard as the static all-pairs shortest-paths problem.  ...  (ii) A randomized fully-dynamic algorithm for the all-pairs shortestpaths problem in directed unweighted graphs with an amortized update time ofÕ(m √ n) and a worst case query time is O(n 3/4 ).  ...  (For steps in this direction, but for the approximate dynamic APSP problem, see [2, 3, 22] .) Fig. 2 . 2 The new fully dynamic all-pairs shortest paths algorithm.  ... 
doi:10.1007/978-3-540-30140-0_52 fatcat:ekwwih5dcfe6hjfntk7r24mnou

On Dynamic Shortest Paths Problems

Liam Roditty, Uri Zwick
2010 Algorithmica  
directed or undirected graphs, are, in a strong sense, at least as hard as the static all-pairs shortest-paths problem.  ...  (ii) A randomized fully-dynamic algorithm for the all-pairs shortestpaths problem in directed unweighted graphs with an amortized update time ofÕ(m √ n) and a worst case query time is O(n 3/4 ).  ...  (For steps in this direction, but for the approximate dynamic APSP problem, see [2, 3, 22] .) Fig. 2 . 2 The new fully dynamic all-pairs shortest paths algorithm.  ... 
doi:10.1007/s00453-010-9401-5 fatcat:2pf45vg5zrg4pmtlxp5ewidsua

A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs

P. N. Klein, S. Subramanian
1998 Algorithmica  
In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks.  ...  Given an error parameter ε such that 0 < ε, our algorithm maintains approximate all-pairs shortest paths in an undirected planar graph G with nonnegative edge lengths.  ...  We are grateful to the referees for their comments and for pointing out an error in an earlier version of the document.  ... 
doi:10.1007/pl00009223 fatcat:vrmwlmlchjdx3fugevbo4eshtu

Algorithms and Hardness for Diameter in Dynamic Graphs

Bertie Ancona, Monika Henzinger, Liam Roditty, Virginia Vassilevska Williams, Nicole Wein, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
For instance, a nearly (3/2 + )-approximation to Diameter in directed or undirected n-vertex, medge graphs can be maintained decrementally in total time m 1+o(1) √ n/ 2 .  ...  While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each update or from solving dynamic All-Pairs  ...  Introduction Computing the shortest paths distances between all pairs of vertices in a graph, the All-Pairs Shortest Paths (APSP) problem, has been studied since the beginning of computer science as a  ... 
doi:10.4230/lipics.icalp.2019.13 dblp:conf/icalp/AnconaHRWW19 fatcat:bg2j3huworg7jbf3lt2clk2clm

Deterministic Partially Dynamic Single Source Shortest Paths in Weighted Graphs [article]

Aaron Bernstein
2017 arXiv   pre-print
In this paper we consider the decremental single-source shortest paths (SSSP) problem, where given a graph G and a source node s the goal is to maintain shortest distances between s and all other nodes  ...  Their classic algorithm was the state of the art for the decremental SSSP problem for three decades, even when approximate shortest paths are allowed.  ...  Finally, we recall from the introduction that all existing deterministic o(mn) results including ours are only able to return approximate shortest distances, not the paths themselves.  ... 
arXiv:1705.10097v1 fatcat:vkuv5qzovnhzbd3xvpufheps6q

Improved Approximation for Orienting Mixed Graphs [article]

Iftah Gamzu, Moti Medina
2012 arXiv   pre-print
The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that admit a directed source-target path.  ...  An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs.  ...  They also proposed an exact dynamic-programming algorithm for the special case of path graphs, and a Ω(1/ log n)approximation algorithm for the general problem.  ... 
arXiv:1204.0219v1 fatcat:ki5fsv74mrcrbdh2sktyxl6fd4

Conditional Hardness for Sensitivity Problems [article]

Monika Henzinger, Andrea Lincoln, Stefan Neumann, Virginia Vassilevska Williams
2017 arXiv   pre-print
We give more lower bounds under the Strong Exponential Time Hypothesis and the All Pairs Shortest Paths Conjecture.  ...  Finally, we give the first algorithm for the (1 + ϵ)-approximate radius, diameter, and eccentricity problems in directed or undirected unweighted graphs in case of single edges failures.  ...  st shortest paths in undirected unweighted graphs with sensitivity 2, 5. (3/2 − ε)-approximate ss shortest paths in undirected unweighted graphs with sensitivity 1, 6. static (5/3 − ε)-approximate ap  ... 
arXiv:1703.01638v1 fatcat:udwtdffcebbijku3zkctq4x4ii

Dynamic Approximate Shortest Paths and Beyond: Subquadratic and Worst-Case Update Time [article]

Jan van den Brand, Danupon Nanongkai
2019 arXiv   pre-print
This query is rather general and captures several versions of the dynamic shortest paths problem.  ...  Our algorithm leads to answers for some open problems for Single-Source and All-Pairs Shortest Paths (SSSP and APSP), as well as for Diameter, Radius, and Eccentricities. Below are some highlights.  ...  If every pair has distance at most n s , then the diameter is smaller. In that case, we simply binary search for it.  ... 
arXiv:1909.10850v2 fatcat:xecognte6jbupk2r6slt4za25u

Fully-Dynamic Approximation of Betweenness Centrality [chapter]

Elisabetta Bergamini, Henning Meyerhenke
2015 Lecture Notes in Computer Science  
Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths.  ...  In particular, we propose a new upper bound on the vertex diameter for weighted undirected graphs.  ...  We thank Moritz von Looz for providing the synthetic dynamic networks and the numerous contributors to the NetworKit project.  ... 
doi:10.1007/978-3-662-48350-3_14 fatcat:e332kxucpfefrg6jk3vsad7o6y

On the Complexity of Weight-Dynamic Network Algorithms [article]

Monika Henzinger, Ami Paz, Stefan Schmid
2021 arXiv   pre-print
While prior work on dynamic graph algorithms focuses on link insertions and deletions, we are interested in the practical problem of link weight changes.  ...  We specifically investigate optimizations related to traffic engineering (namely shortest paths and maximum flow computations), but also consider spanning tree and matching applications.  ...  Any algorithm that maintains distances between all pairs of nodes (all pairs shortest paths, or APSP) or between a source and all other nodes (single-source shortest paths, or SSSP) can also be used to  ... 
arXiv:2105.13172v2 fatcat:zcfe4uc3sragrch4l7w5jbe2fu

An Efficient Algorithm for All Pair Shortest Paths

P K Singh, Rajendra Kumar, Vijay Shankar Pandey
2010 International Journal of Computer and Electrical Engineering  
In this paper, an all pairs optimized shortest path algorithm is presented for an unweighted and undirected graph with some additive error of at most 2.This algorithm can be extended for weighted graph  ...  The run time of the algorithm is of order Ο(n5/2), where n is the number of vertices present in the graph. This algorithm is much simpler than the existing algorithms.  ...  can be solved in Õ(√n 3 M(n)) time and the all pairs shortest paths problem for unweighted undirected graphs can be solved in Õ(M(n)) time.  ... 
doi:10.7763/ijcee.2010.v2.263 fatcat:ihfyfbcifnd4pimsmrdvocpnci

An Optimized All pair Shortest Paths Algorithm

Vijay Shankar Pandey, Rajendra Kumar, Dr. P K Singh
2010 International Journal of Computer Applications  
In this paper, we present an algorithm to compute all pairs optimized shortest paths in an unweighted and undirected graph with some additive error of at most 2.This algorithm can be extended for weighted  ...  The algorithm runs in n 5/2 ) times, where n is the number of vertices in the graph. This algorithm is much simpler than the existing algorithms.  ...  pairs shortest paths algorithm All pairs optimized shortest paths algorithmFor unweighted and undirected graphs Baswana et al.  ... 
doi:10.5120/640-896 fatcat:xpjlvzdm5nbvfivb26z42dxnry

Approximating Betweenness Centrality in Fully-dynamic Networks [article]

Elisabetta Bergamini, Henning Meyerhenke
2015 arXiv   pre-print
of the vertex diameter in undirected graphs, and (iii) an algorithm with lower time complexity for updating single-source shortest paths in unweighted graphs after a batch of edge actions.  ...  Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths.  ...  Second, changes in the VD approximation can require to sample new paths and therefore increase the running time of DA (and DAW).  ... 
arXiv:1510.07971v1 fatcat:hwohlqkl75htvm2kzsq4fa4wce
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