Improving exact algorithms for MAX-2-SAT

Authors:
Haiou Shen;Hantao Zhang
Affiliations:
Computer Science Department, The University of Iowa, Iowa City, USA 52242;Computer Science Department, The University of Iowa, Iowa City, USA 52242
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2005

Citing 10
Cited 5

Algorithms for the maximum satisfiability problem

Computing
Parameterizing above guaranteed values: MaxSat and MaxCut

Journal of Algorithms
New upper bounds for maximum satisfiability

Journal of Algorithms
A machine program for theorem-proving

Communications of the ACM
sub-SAT: a formulation for relaxed boolean satisfiability with applications in routing

Proceedings of the 2002 international symposium on Physical design
New Worst-Case Upper Bounds for SAT

Journal of Automated Reasoning
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search

Theoretical Computer Science
Counting Models Using Connected Components

Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT

Discrete Applied Mathematics - The renesse issue on satisfiability
Study of lower bound functions for MAX-2-SAT

AAAI'04 Proceedings of the 19th national conference on Artifical intelligence

Redundancy in logic II: 2CNF and Horn propositional formulae

Artificial Intelligence
Detecting disjoint inconsistent subformulas for computing lower bounds for Max-SAT

AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
New inference rules for Max-SAT

Journal of Artificial Intelligence Research
A complete calculus for Max-SAT

SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Iterative and core-guided MaxSAT solving: A survey and assessment

Constraints

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study three new techniques that will speed up the branch-and-bound algorithm for the MAX-2-SAT problem: The first technique is a group of new lower bound functions for the algorithm and we show that these functions are admissible and consistently better than other known lower bound functions. The other two techniques are based on the strongly connected components of the implication graph of a 2CNF formula: One uses the graph to simplify the formula and the other uses the graph to design a new variable ordering. The experiments show that the simplification can reduce the size of the input substantially no matter what is the clause-to-variable ratio and that the new variable ordering performs much better when the clause-to-variable ratio is less than 2. A direct outcome of this research is a high-performance implementation of an exact algorithm for MAX-2-SAT which outperforms any implementation we know about in the same category. We also show that our implementation is a feasible and effective tool to solve large instances of the Max-Cut problem in graph theory.