Solving Weighted Max-SAT Problems in a Reduced Search Space: A Performance Analysis

We analyze, in this work, the performance of a recently introduced weighted Max-SAT solver, Clone, in the Max-SAT evaluation 2007. Clone utilizes a novel bound computation based on formula compilation that allows it to search in a reduced search space. We study how additional techniques from the SAT and Max-SAT literature affect the performance of Clone on problems from the evaluation. We then perform further investigations on factors that may affect the performance of leading Max-SAT solvers. We empirically identify two properties of weighted Max-SAT problems that can be used to adjust the difficulty level of the problems with respect to the considered solvers.

[1]  Mark W. Krentel.  The complexity of optimization problems , 1986, STOC '86.

[2]  Rina Dechter,et al.  Constraint Processing , 1995, Lecture Notes in Computer Science.

[3]  Uue Kjjrull.  Triangulation of Graphs { Algorithms Giving Small Total State Space Triangulation of Graphs { Algorithms Giving Small Total State Space , 1990 .

[4]  Sharad Malik,et al.  On Solving the Partial MAX-SAT Problem , 2006, SAT.

[5]  Adnan Darwiche,et al.  New Advances in Compiling CNF into Decomposable Negation Normal Form , 2004, ECAI.

[6]  Josep Argelich,et al.  A Preprocessor for Max-SAT Solvers , 2008, SAT.

[7]  Pierre Marquis,et al.  A Knowledge Compilation Map , 2002, J. Artif. Intell. Res..

[8]  D. Rose.  A GRAPH-THEORETIC STUDY OF THE NUMERICAL SOLUTION OF SPARSE POSITIVE DEFINITE SYSTEMS OF LINEAR EQUATIONS , 1972 .

[9]  Ronald C. Read,et al.  Graph theory and computing , 1972 .

[10]  Adnan Darwiche,et al.  Clone: Solving Weighted Max-SAT in a Reduced Search Space , 2007, Australian Conference on Artificial Intelligence.

[11]  Yahiko Kambayashi,et al.  Database Queries as Combinatorial Optimization Problems , 1996, CODAS.

[12]  Simon de Givry,et al.  A logical approach to efficient Max-SAT solving , 2006, Artif. Intell..

[13]  Gregory F. Cooper,et al.  Probabilistic inference in multiply connected belief networks using loop cutsets , 1990, Int. J. Approx. Reason..

[14]  Teresa Alsinet,et al.  A Max-SAT Solver with Lazy Data Structures , 2004, IBERAMIA.

[15]  Jinchang Wang.  A branching heuristic for testing propositional satisfiability , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[16]  Lawrence Ryan.  Efficient algorithms for clause-learning SAT solvers , 2004 .

[17]  James D. Park.  Using weighted MAX-SAT engines to solve MPE , 2002, AAAI/IAAI.

[18]  Byungki Cha,et al.  Local Search Algorithms for Partial MAXSAT , 1997, AAAI/IAAI.

[19]  Kaile Su,et al.  Exploiting Inference Rules to Compute Lower Bounds for MAX-SAT Solving , 2007, IJCAI.

[20]  Joao Marques-Silva,et al.  GRASP: A Search Algorithm for Propositional Satisfiability , 1999, IEEE Trans. Computers.

[21]  Hector Geffner,et al.  Structural Relaxations by Variable Renaming and Their Compilation for Solving MinCostSAT , 2007, CP.

[22]  Adnan Darwiche,et al.  Decomposable negation normal form , 2001, JACM.

[23]  Olivier Coudert,et al.  On solving covering problems , 1996, DAC '96.

[24]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.

[25]  Roberto J. Bayardo,et al.  Using CSP Look-Back Techniques to Solve Real-World SAT Instances , 1997, AAAI/IAAI.

[26]  Gerald J. Sussman,et al.  Forward Reasoning and Dependency-Directed Backtracking in a System for Computer-Aided Circuit Analysis , 1976, Artif. Intell..

[27]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[28]  Paul D. Seymour,et al.  Graph Minors. II. Algorithmic Aspects of Tree-Width , 1986, J. Algorithms.

[29]  Albert Oliveras,et al.  MiniMaxSat: A New Weighted Max-SAT Solver , 2007, SAT.

[30]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[31]  Josep Argelich,et al.  Partial Max-SAT Solvers with Clause Learning , 2007, SAT.

[32]  Sharad Malik,et al.  Efficient conflict driven learning in a Boolean satisfiability solver , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[33]  Adnan Darwiche,et al.  Node Splitting: A Scheme for Generating Upper Bounds in Bayesian Networks , 2007, UAI.

[34]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[35]  Pierre Marquis,et al.  Compiling propositional weighted bases , 2004, Artif. Intell..

[36]  Felip Manyà,et al.  Exploiting Unit Propagation to Compute Lower Bounds in Branch and Bound Max-SAT Solvers , 2005, CP.

[37]  Felip Manyà,et al.  New Inference Rules for Max-SAT , 2007, J. Artif. Intell. Res..

[38]  Matthias F. Stallmann,et al.  Optimization algorithms for the minimum-cost satisfiability problem , 2004 .

[39]  Josep Argelich,et al.  Exact Max-SAT solvers for over-constrained problems , 2006, J. Heuristics.

[40]  Simon de Givry,et al.  Existential arc consistency: Getting closer to full arc consistency in weighted CSPs , 2005, IJCAI.

[41]  Javier Larrosa,et al.  Resolution in Max-SAT and its relation to local consistency in weighted CSPs , 2005, IJCAI.

[42]  Kenneth L. McMillan,et al.  Applying SAT Methods in Unbounded Symbolic Model Checking , 2002, CAV.