Finding large independent sets of hypergraphs in parallel

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 &agr;k(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 &agr;k (H). They also show that &agr;k (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 &agr;k(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.