An efficient parallel strategy for recognizing series-parallel graphs

Abstract

An efficient parallel algorithm for recognizing series-parallel (SP) graphs on a CRCW PRAM is presented. The time complexity of the algorithm is O(log n), and the number of processors used is O((m + n) loglog n/log n), where n is the number of vertices and m is the number of edges of the input graph. This paper develops a new methodology of recognition for SP graphs, based on open ear decomposition, that improves the complexity found in previous results. Another emphasis in our algorithms is placed on the construction of decomposition trees for SP graphs. Some interesting properties of SP graphs are derived in order to facilitate fast parallel processing.