Analysis of parallel algorithms for finding a maximal independent set in a random hypergraph

Abstract

It is well known [9] that finding a maximal independent set in a graph is in class NC and [10] that finding a maximal independent set in a hypergraph with fixed dimension is in RNC. It is not known whether this latter problem remains in NC when the dimension is part of the input. We will study the problem when the problem instances are randomly chosen. It was shown in [6] that the expected running time of a simple parallel algorithm for finding the lexicographically first maximal independent set (Ifmis) in a random simple graph is logarithmic in the input size. In this paper, we will prove a generalization of this result. We show that if a random k-uniform hypergraph has vertex set {1, 2, …, n} and its edges are chosen independently with probability p from the set of (nk) possible edges, then our algorithm finds the Ifmis in O() expected time. The hidden constant is independent of k, p. © 1996 John Wiley & Sons, Inc. Random Struct. Alg., 9, 359–377 (1996)