New Results on Monotone Dualization and Generating Hypergraph Transversals
Abstract
We consider the problem of dualizing a monotone CNF (equivalently, computing all minimal transversals of a hypergraph), whose associated decision problem is a prominent open problem in NPcompleteness. We present a number of new polynomial time resp. outputpolynomial time results for significant cases, which largely advance the tractability frontier and improve on previous results. Furthermore, we show that duality of two monotone CNFs can be disproved with limited nondeterminism. More precisely, this is feasible in polynomial time with O(chi(n) * log n) suitably guessed bits, where chi(n) is given by \chi(n)^chi(n) = n; note that chi(n) = o(log n). This result sheds new light on the complexity of this important problem.
 Publication:

arXiv eprints
 Pub Date:
 April 2002
 arXiv:
 arXiv:cs/0204009
 Bibcode:
 2002cs........4009E
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Complexity;
 F.2.2;
 F.1.3;
 G.2.1;
 G.2.2
 EPrint:
 Removed some minor errors. A shorter version of this paper appears in: Proceedings of the 34th ACM Symposium on Theory of Computing (STOC02), May 1921, 2002, Montreal, Quebec, Canada