Approximate Algorithms and Heuristics for MAX-SAT

In the Maximum Satisfiability (MAX-SAT) problem one is given a Boolean formula in conjunctive normal form, i.e., as a conjunction of clauses, each clause being a disjunction. The task is to find an assignment of truth values to the variables that satisfies the maximum number of clauses.

[1]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[2]  J. K. Lowe,et al.  Some results and experiments in programming techniques for propositional logic , 1986, Comput. Oper. Res..

[3]  Hector J. Levesque,et al.  Hard and Easy Distributions of SAT Problems , 1992, AAAI.

[4]  Bart Selman,et al.  Domain-Independent Extensions to GSAT: Solving Large Structured Satisfiability Problems , 1993, IJCAI.

[5]  Mauricio G. C. Resende,et al.  Computational experience with an interior point algorithm on the satisfiability problem , 1990, IPCO.

[6]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[7]  Alan M. Frieze,et al.  Analysis of Two Simple Heuristics on a Random Instance of k-SAT , 1996, J. Algorithms.

[8]  John Franco,et al.  Probabilistic analysis of the Davis Putnam procedure for solving the satisfiability problem , 1983, Discret. Appl. Math..

[9]  Strengthening Lagrangian Bounds for the Max-sat Problem , 1996 .

[10]  David P. Williamson,et al.  New 3/4-Approximation Algorithms for the Maximum Satisfiability Problem , 1994, SIAM J. Discret. Math..

[11]  Jianer Chen,et al.  Tight bound on Johnson's algorithm for Max-SAT , 1997, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference.

[12]  Andreas Goerdt,et al.  A Threshold for Unsatisfiability , 1992, MFCS.

[13]  Alan M. Frieze,et al.  On the satisfiability and maximum satisfiability of random 3-CNF formulas , 1993, SODA '93.

[14]  Giorgio Ausiello,et al.  Theoretical Computer Science Approximate Solution of Np Optimization Problems * , 2022 .

[15]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.

[16]  Alessandro Panconesi,et al.  Completeness in Approximation Classes , 1989, FCT.

[17]  Takao Asano,et al.  Approximation algorithms for MAX SAT: Yannakakis vs. Goemans-Williamson , 1997, Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems.

[18]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[19]  Bart Selman,et al.  An Empirical Study of Greedy Local Search for Satisfiability Testing , 1993, AAAI.

[20]  Jack Minker,et al.  Logic and Databases: A Deductive Approach , 1984, CSUR.

[21]  C.H. Papadimitriou,et al.  On selecting a satisfying truth assignment , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[22]  Walton A. Perkins,et al.  Checking an Expert Systems Knowledge Base for Consistency and Completeness , 1985, IJCAI.

[23]  Bart Selman,et al.  Local search strategies for satisfiability testing , 1993, Cliques, Coloring, and Satisfiability.

[24]  Brigitte Jaumard,et al.  Tabu search and a quadratic relaxation for the Satisfiability problem , 1993, Cliques, Coloring, and Satisfiability.

[25]  Maurizio Martelli,et al.  Integrity Constraints for Logic Databases , 1985, J. Log. Program..

[26]  Hector J. Levesque,et al.  A New Method for Solving Hard Satisfiability Problems , 1992, AAAI.

[27]  Pierre Hansen,et al.  Roof duality, complementation and persistency in quadratic 0–1 optimization , 1984, Math. Program..

[28]  Ming-Te Chao,et al.  Probabilistic Analysis of Two Heuristics for the 3-Satisfiability Problem , 1986, SIAM J. Comput..

[29]  Oliver Kullmann,et al.  Deciding propositional tautologies: Algorithms and their complexity , 1997 .

[30]  Roberto Battiti,et al.  Reactive search, a history-sensitive heuristic for MAX-SAT , 1997, JEAL.

[31]  Mihalis Yannakakis,et al.  On the approximation of maximum satisfiability , 1992, SODA '92.

[32]  Vishwani D. Agrawal,et al.  Neural net and Boolean satisfiability models of logic circuits , 1990, IEEE Design & Test of Computers.

[33]  Paola Alimonti.  New Local Search Approximation Techniques for Maximum Generalized Satisfiability Problems , 1994, CIAC.

[34]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[35]  Yacine Boufkhad,et al.  A General Upper Bound for the Satisfiability Threshold of Random r-SAT Formulae , 1997, J. Algorithms.

[36]  Panos M. Pardalos,et al.  Satisfiability Problem: Theory and Applications , 1997 .

[37]  David P. Williamson,et al.  Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming , 1995, JACM.

[38]  Jun Gu,et al.  Convergence Properties of Optimization Algorithms for the SAT Problem , 1996, IEEE Trans. Computers.

[39]  Roberto Battiti,et al.  The Reactive Tabu Search , 1994, INFORMS J. Comput..

[40]  Toby Walsh,et al.  An Empirical Analysis of Search in GSAT , 1993, J. Artif. Intell. Res..

[41]  Toby Walsh,et al.  Towards an Understanding of Hill-Climbing Procedures for SAT , 1993, AAAI.

[42]  Giorgio Ausiello,et al.  Lattice theoretic ordering properties for NP-complete optimization problems , 1981, Fundam. Informaticae.

[43]  Uriel Feige,et al.  Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT , 1995, Proceedings Third Israel Symposium on the Theory of Computing and Systems.

[44]  Jun Gu,et al.  Asynchronous circuit synthesis with Boolean satisfiability , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[45]  Christos H. Papadimitriou,et al.  On the Greedy Algorithm for Satisfiability , 1992, Information Processing Letters.

[46]  Mauricio G. C. Resende,et al.  A continuous approach to inductive inference , 1992, Math. Program..

[47]  Giorgio Ausiello,et al.  Local Search, Reducibility and Approximability of NP-Optimization Problems , 1995, Inf. Process. Lett..

[48]  Sanjeev Arora,et al.  Probabilistic checking of proofs; a new characterization of NP , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[49]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[50]  James L. Johnson.  A Neural Network Approach to the 3-Satisfiability Problem , 1989, J. Parallel Distributed Comput..

[51]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[52]  William H. Cunningham,et al.  A linear programming and rounding approach to max 2-sat , 1993, Cliques, Coloring, and Satisfiability.

[53]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[54]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[55]  Takao Asano,et al.  Approximation Algorithms for the Maximum Satisfiability Problem , 1996, Nord. J. Comput..

[56]  Steven Minton,et al.  Solving Large-Scale Constraint-Satisfaction and Scheduling Problems Using a Heuristic Repair Method , 1990, AAAI.

[57]  Bruce A. Reed,et al.  Mick gets some (the odds are on his side) (satisfiability) , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[58]  Paul G. Spirakis,et al.  Tail bounds for occupancy and the satisfiability threshold conjecture , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[59]  Luca Trevisan.  Approximating Satisfiable Satisfiability Problems , 2000, Algorithmica.

[60]  L. Kirousis,et al.  Approximating the unsatisfiability threshold of random formulas , 1998 .

[61]  Jun Gu,et al.  Efficient local search for very large-scale satisfiability problems , 1992, SGAR.

[62]  Jun Gu,et al.  Global Optimization for Satisfiability (SAT) Problem , 1994, IEEE Trans. Knowl. Data Eng..

[63]  Panos M. Pardalos,et al.  Approximate solution of weighted MAX-SAT problems using GRASP , 1996, Satisfiability Problem: Theory and Applications.

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

[65]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[66]  Uri Zwick,et al.  A 7/8-approximation algorithm for MAX 3SAT? , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[67]  Endre Szemerédi,et al.  Many hard examples for resolution , 1988, JACM.

[68]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[69]  David G. Mitchell,et al.  Finding hard instances of the satisfiability problem: A survey , 1996, Satisfiability Problem: Theory and Applications.

[70]  Donald W. Loveland,et al.  Automated theorem proving: a logical basis , 1978, Fundamental studies in computer science.

[71]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[72]  Evangelos Kranakis,et al.  Approximating the Unsatisfiability Threshold of Random Formulas (Extended Abstract) , 1996, ESA.

[73]  P. Orponen,et al.  On Approximation Preserving Reductions: Complete Problems and Robust Measures (Revised Version) , 1987 .

[74]  Jun Gu,et al.  Algorithms for the satisfiability (SAT) problem: A survey , 1996, Satisfiability Problem: Theory and Applications.

[75]  Mauricio G. C. Resende,et al.  A GRASP for satisfiability , 1993, Cliques, Coloring, and Satisfiability.

[76]  William M. Spears,et al.  Simulated annealing for hard satisfiability problems , 1993, Cliques, Coloring, and Satisfiability.

[77]  J. Hooker.  Resolution vs. cutting plane solution of inference problems: Some computational experience , 1988 .