Finding large independent sets of hypergraphs in parallel

Abstract

A basic problem in hypergraphs is that of finding a large independent set-one of guaranteed size-in a given hypergraph. Understanding the parallel complexity of this and related independent set problems on hypergraphs is a fundamental open issue in parallel computation. Caro and Tuza (J. Graph Theory, Vol. 15, pp. 99-107, 1991) have shown a certain lower bound αk(H) on the size of a maximum independent set in a given k-uniform hypergraph H, and have also presented an efficien sequential algorithm to find an independent set of size αk (H). They also show that αk (H) is the size of the maximum independent set for various hypergraph families. Here, we develop the first RNC algorithm to find an independent set of size αk(H), and also derandomize it for various special cases. We also present lower bounds on independent set size and corresponding RNC algorithms for non-uniform hypergraphs.