An Algorithm for Hinge Vertex Problem on Circular Trapezoid Graphs

Abstract

Let G = (V, E) be a simple connected graph. A vertex u ∈ V is called a hinge vertex if there exist two vertices x and y in G whose distance increases when u is removed. Finding all hinge vertices of a given graph is called the hinge vertex problem. This problem can be applied to improve the stability and robustness of communication network systems. In a number of graph problems, it is known that more efficient sequential or parallel algorithms can be developed by restricting classes of graphs. Circular trapezoid graphs are proper super-classes of trapezoid graphs. In this paper, we propose an O(n 2 ) time algorithm for the hinge vertex problem of circular trapezoid 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.…”