DIMACS TR: 2000-21

An Incremental RNC Algorithm for Generating All Maximal Independent Sets in Hypergraphs of Bounded Dimension

Authors: E. Boros, K. Elbassioni, V. Gurvich and L. Khachiyan


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.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-21.ps.gz
DIMACS Home Page