TY - GEN

T1 - Faster algorithms for computing maximal 2-connected subgraphs in sparse directed graphs

AU - Chechik, Shiri

AU - Hanseny, Thomas Dueholm

AU - Italiano, Giuseppe F.

AU - Loitzenbauer, Veronika

AU - Parotsidis, Nikos

N1 - Publisher Copyright:
Copyright © by SIAM.

PY - 2017

Y1 - 2017

N2 - Connectivity related concepts are of fundamental interest in graph theory. The area has received extensive attention over four decades, but many problems remain unsolved, especially for directed graphs. A directed graph is 2-edge-connected (resp., 2-vertex-connected) if the removal of any edge (resp., vertex) leaves the graph strongly connected. In this paper we present improved algorithms for computing the maximal 2-edge and 2- vertex-connected subgraphs of a given directed graph. These problems were first studied more than 35 years ago, with eO(mn) time algorithms for graphs with m edges and n vertices being known since the late 1980s. In contrast, the same problems for undirected graphs are known to be solvable in linear time. Henzinger et al. [ICALP 2015] recently introduced O(n2) time algo- rithms for the directed case, thus improving the running times for dense graphs. Our new algorithms run in time O(m3=2), which further improves the running times for sparse graphs. The notion of 2-connectivity naturally generalizes to k-connectivity for k > 2. For constant values of k, we extend one of our algorithms to compute the maximal k-edge-connected in time O(m3=2 log n), improving again for sparse graphs the best known algorithm by Henzinger et al. [ICALP 2015] that runs in O(n2 log n) time.

AB - Connectivity related concepts are of fundamental interest in graph theory. The area has received extensive attention over four decades, but many problems remain unsolved, especially for directed graphs. A directed graph is 2-edge-connected (resp., 2-vertex-connected) if the removal of any edge (resp., vertex) leaves the graph strongly connected. In this paper we present improved algorithms for computing the maximal 2-edge and 2- vertex-connected subgraphs of a given directed graph. These problems were first studied more than 35 years ago, with eO(mn) time algorithms for graphs with m edges and n vertices being known since the late 1980s. In contrast, the same problems for undirected graphs are known to be solvable in linear time. Henzinger et al. [ICALP 2015] recently introduced O(n2) time algo- rithms for the directed case, thus improving the running times for dense graphs. Our new algorithms run in time O(m3=2), which further improves the running times for sparse graphs. The notion of 2-connectivity naturally generalizes to k-connectivity for k > 2. For constant values of k, we extend one of our algorithms to compute the maximal k-edge-connected in time O(m3=2 log n), improving again for sparse graphs the best known algorithm by Henzinger et al. [ICALP 2015] that runs in O(n2 log n) time.

UR - http://www.scopus.com/inward/record.url?scp=85016205745&partnerID=8YFLogxK

U2 - 10.1137/1.9781611974782.124

DO - 10.1137/1.9781611974782.124

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AN - SCOPUS:85016205745

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1900

EP - 1918

BT - 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017

A2 - Klein, Philip N.

PB - Association for Computing Machinery

T2 - 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017

Y2 - 16 January 2017 through 19 January 2017

ER -