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COMPUTING MANY MAXIMAL INDEPENDENT SETS FOR HYPERGRAPHS IN PARALLEL

    A hypergraph is called uniformly δ-sparse if for every nonempty subset X ⊆ V of vertices, the average degree of the sub-hypergraph of induced by X is at most δ. We show that there is a deterministic algorithm that, given a uniformly δ-sparse hypergraph , and a positive integer k, outputs k or all minimal transversals for in O(δlog(1 + k)polylog(δ|V|))-time using |V|O(logδ)kO(δ) processors. Equivalently, the algorithm can be used to compute in parallel k or all maximal independent sets for .

    This research was supported in part by the National Science Foundation, grant, IIS-0118635. The third author is also grateful for the partial support by DIMACS, the National Science Foundation's Center for Discrete Mathematics and Theoretical Computer Science.

    References