›› 2013, Vol. 28 ›› Issue (2): 232-246.doi: 10.1007/s11390-013-1325-5

• Theoretical Computer Science • Previous Articles     Next Articles

A Taxonomy of Exact Methods for Partial Max-SAT

Mohamed El Bachir Menai and Tasniem Nasser Al-Yahya   

  1. Department of Computer Science, College of Computer and Information Sciences, King Saud University, P.O.Box 51178Riyadh 11543, Saudi Arabia
  • Received:2012-01-10 Revised:2012-08-30 Online:2013-03-05 Published:2013-03-05
  • Supported by:

    This work was supported by the Research Center of College of Computer and Information Sciences at King Saud University, Saudi Arabia.

Partial Maximum Boolean Satisfiability (Partial Max-SAT or PMSAT) is an optimization variant of Boolean satisfiability (SAT) problem, in which a variable assignment is required to satisfy all hard clauses and a maximum number of soft clauses in a Boolean formula. PMSAT is considered as an interesting encoding domain to many real-life problems for which a solution is acceptable even if some constraints are violated. Amongst the problems that can be formulated as such are planning and scheduling. New insights into the study of PMSAT problem have been gained since the introduction of the Max-SAT evaluations in 2006. Indeed, several PMSAT exact solvers have been developed based mainly on the Davis- Putnam-Logemann-Loveland (DPLL) procedure and Branch and Bound (B&B) algorithms. In this paper, we investigate and analyze a number of exact methods for PMSAT. We propose a taxonomy of the main exact methods within a general framework that integrates their various techniques into a unified perspective. We show its effectiveness by using it to classify PMSAT exact solvers which participated in the 2007~2011 Max-SAT evaluations, emphasizing on the most promising research directions.

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