2-vertex connectivity in directed graphs

Given a directed graph, two vertices v and w are 2-vertex-connected if there are two internally vertex-disjoint paths from v to w and two internally vertex-disjoint paths from w to v. In this paper, we show how to compute this relation in O ( m + n ) time, where n is the number of vertices and m is the number of edges of the graph. As a side result, we show how to build in linear time an O ( n ) -space data structure, which can answer in constant time queries on whether any two vertices are 2-vertex-connected. Additionally, when two query vertices v and w are not 2-vertex-connected, our data structure can produce in constant time a “witness” of this property, by exhibiting a vertex or an edge that is contained in all paths from v to w or in all paths from w to v.

Authors

• Loukas Georgiadis
• Giuseppe F. Italiano
• Luigi Laura
• Nikos Parotsidis

Keywords

• Connectivity
• Directed graph
• Dominators
• Flow graph
• Strong articulation points