Warning Propagation Algorithm for the MAX-3-SAT Problem

Message propagation algorithms are widely used in approximate inference e.g. Cyber-Social Data Processing and Intelligence Mining. Especially, these algorithms enable hard region become narrower and thus they are very effective in solving satisfiability problems. Warning Propagation algorithm is one kind of basic message propagation algorithms. Based on this Warning Propagation algorithm, we designed a WPY algorithm to solve the MAX-3-SAT problem. We obtained a set of stable warning information, and the value of the partial variable is decided by using the stable set with high probability. Finally, the experiment results show that the WPY algorithm can effectively solve the random MAX-3-SAT instances.

[1]  Riccardo Zecchina,et al.  Survey propagation: An algorithm for satisfiability , 2002, Random Struct. Algorithms.

[2]  S Kirkpatrick,et al.  Critical Behavior in the Satisfiability of Random Boolean Expressions , 1994, Science.

[3]  M. Mézard,et al.  Random K-satisfiability problem: from an analytic solution to an efficient algorithm. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  John W. Fisher,et al.  Loopy Belief Propagation: Convergence and Effects of Message Errors , 2005, J. Mach. Learn. Res..

[5]  Yair Weiss,et al.  Correctness of Local Probability Propagation in Graphical Models with Loops , 2000, Neural Computation.

[6]  William T. Freeman,et al.  Correctness of Belief Propagation in Gaussian Graphical Models of Arbitrary Topology , 1999, Neural Computation.

[7]  Erik Aurell,et al.  Comparing Beliefs, Surveys, and Random Walks , 2004, NIPS.

[8]  Kamiel Cornelissen,et al.  Smoothed Analysis of Belief Propagation for Minimum-Cost Flow and Matching , 2013, WALCOM.

[9]  Olivier Dubois,et al.  Typical random 3-SAT formulae and the satisfiability threshold , 2000, SODA '00.

[10]  Sekhar Tatikonda,et al.  Loopy Belief Propogation and Gibbs Measures , 2002, UAI.

[11]  Holger H. Hoos,et al.  UBCSAT: An Implementation and Experimentation Environment for SLS Algorithms for SAT & MAX-SAT , 2004, SAT.

[12]  Efthimios G. Lalas,et al.  The probabilistic analysis of a greedy satisfiability algorithm , 2006 .

[13]  Tom Heskes,et al.  On the Uniqueness of Loopy Belief Propagation Fixed Points , 2004, Neural Computation.

[14]  Daniela Tuninetti,et al.  Message Error Analysis of Loopy Belief Propagation for the Sum-Product Algorithm , 2010, ArXiv.

[15]  Hilbert J. Kappen,et al.  Sufficient Conditions for Convergence of the Sum–Product Algorithm , 2005, IEEE Transactions on Information Theory.

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

[17]  Martin J. Wainwright,et al.  Stochastic Belief Propagation: A Low-Complexity Alternative to the Sum-Product Algorithm , 2011, IEEE Transactions on Information Theory.

[18]  M. Mézard,et al.  Threshold values of random K-SAT from the cavity method , 2006 .

[19]  Riccardo Zecchina,et al.  Survey and Belief Propagation on Random K-SAT , 2003, SAT.

[20]  Felip Manyà,et al.  Detecting Disjoint Inconsistent Subformulas for Computing Lower Bounds for Max-SAT , 2006, AAAI.

[21]  Martin J. Wainwright,et al.  A new look at survey propagation and its generalizations , 2004, SODA '05.

[22]  William T. Freeman,et al.  Understanding belief propagation and its generalizations , 2003 .

[23]  Devavrat Shah,et al.  Belief propagation for min-cost network flow: convergence & correctness , 2010, SODA '10.

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

[25]  M. Mézard,et al.  The Cavity Method at Zero Temperature , 2002, cond-mat/0207121.