Linear Time Algorithms for Finding Articulation and Hinge Vertices of Circular Permutation Graphs

Abstract

SUMMARYLet G s = (V s , E s ) be a simple connected graph. A vertex v ∈ V s is an articulation vertex if deletion of v and its incident edges from G s disconnects the graph into at least two connected components. Finding all articulation vertices of a given graph is called the articulation vertex problem. A vertex u ∈ V s is called a hinge vertex if there exist any two vertices x and y in G s whose distance increase when u is removed. Finding all hinge vertices of a given graph is called the hinge vertex problem. These problems can be applied to improve the stability and robustness of communication network systems. In this paper, we propose linear time algorithms for the articulation vertex problem and the hinge vertex problem of circular permutation graphs.

Algorithm for the Vertex Connectivity Problem on Circular Trapezoid Graphs

“…By using extended intersection models such as an ECTM, we can determine the start position of an algorithm uniquely and apply the algorithms of the non-circular versions partially. For instance, this method has been applied to develop efficient algorithms for the shortest path query problem [12] [13] and the articulation vertex problem [14] on circular-arc graphs, maximum clique and chromatic number problems [15], the spanning forest problem [16] and the articulation problem [17] on circular permutation graphs, and the spanning tree problem [11] and the hinge vertex problem [18] on circular trapezoid graphs.…”