New Results on Monotone Dualization and Generating Hypergraph Transversals

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, respectively, output-polynomial time results for signif...

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Bibliographic Details
Published in:SIAM journal on computing Vol. 32; no. 2; pp. 514 - 537
Main Authors: Eiter, Thomas, Gottlob, Georg, Makino, Kazuhisa
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2003
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Boolean
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Game theory
Graph theory
Graphs
Information systems. Data bases
Mathematical programming
Mathematics
Memory organisation. Data processing
Order, lattices, ordered algebraic structures
Sciences and techniques of general use
Software
Theoretical computing
Variables
Hypergraph
Knowledge representation
Boolean function
Duality
Computing
Non determinism
Polynomial time
Treewidth
Combinatorial enumeration
Output polynomial algorithm
Database
Transversal computation
NP complete problem
Acyclic graph
Algorithm analysis
ISSN:0097-5397, 1095-7111
Online Access:Get full text
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Summary: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, respectively, 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(log2n/\log log n) suitably guessed bits. This result sheds new light on the complexity of this important problem.
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ISSN:0097-5397
1095-7111
DOI:10.1137/S009753970240639X