An NC algorithm for finding a maximal acyclic set in a graph

Abstract

An acyclic set in an undirected graph G = (V,E) is a set A ⊆ V(G) such that the induced graph on A is acyclic. A maximal acyclic set (MAS) has the further property that no vertex can be added to it without creating a cycle in the induced graph. We present the first NC algorithm that finds an MAS in any graph, running in time O(log4n) using O((m2 + n)/log n) processors on a EREW PRAM, answering questions raised by Chen and He. Our NC algorithm for finding an MAS in a graph relies on a novel NC algorithm for finding a maximal forest in a hypergraph which may be of independent interest.