We show that for hypergraphs of bounded edge size, the problem of extending a given list of maximal independent sets is NC-reducible to the computation of an arbitrary maximal independent set for an induced sub- hypergraph. The latter problem is known to be in RNC. In particular, our reduction yields an incremental RNC dualization algorithm for hypergraphs of bounded edge size, a problem previously known to be solvable in polynomial incremental time. We also give a similar parallel algorithm for the dualization problem on the product of arbitrary lattices which have a bounded number of immediate predecessors for each element.
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