An Efficient Parallel Algorithm for Computing a Maximal Independent Set in a Hypergraph of Dimension 3

The paper considers the problem of computing a maximal independent set in a hypergraph (see 3] and 7]). We present an eecient deterministic NC algorithm for nding a maximal independent set in a hypergraph of dimension 3: the algorithm runs in time O(log 4 n) time on n + m processors of an EREW PRAM and is optimal up to a polylogarithmic factor. Our algorithm adapts the technique of Goldberg and Spencer ((5]) for nding a maximal independent set in a graph (or hypergraph of dimension 2). It is the rst eecient NC algorithm for nding a maximal independent set in a hypergraph of dimension greater than 2.