Optimal algorithms for computing articulation points and some related problems on a circular-arc graph

Abstract

We consider the following three problems when we are given a set of n circular-arcs: (1) the articulation points problem, (2) the bridges problem and (3) the biconnected components problem. We first give several optimal O( n log n) time sequential algorithms for these problems, if the endpoints of the arcs are unsorted. If the endpoints are presorted, our algorithms can be solved in O( n) time. The algorithms proposed are suitable to be implemented on a parallel computation model. On the EREW PRAM model, our algorithms run either in an O(log n) time using O( n) processors for the unsorted case or in an O(log n) time using O( n log n ) processors for the sorted case. The proposed algorithms for both cases are optimal speed-up.