New Results on Monotone Dualization and Generating Hypergraph Transversals

Details New Results on Monotone Dualization and Generating Hypergraph Transversals New Results on Monotone Dualization and Generating Hypergraph Transversals

2002-04-04

arxiv.org/abs/cs/0204009v3

Computer Science

Data Structures and Algorithms

Removed some minor errors. A shorter version of this paper appears in: Proceedings of the 34th ACM Symposium on Theory of Comp

Scientific paper

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 NP-completeness. We present a number of new polynomial time resp. output-polynomial 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.

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