Approximating Satisfiable Satisfiability Problems (Extended Abstract)

We study the approximability of the Maximum Satisfiability Problem (MAX SAT) and of the boolean k -ary Constraint Satisfaction Problem (MAX k CSP) restricted to satisfiable instances. For both problems we improve on the performance ratios of known algorithms for the unrestricted case.

[1]  László Lovász,et al.  Interactive proofs and the hardness of approximating cliques , 1996, JACM.

[2]  Mihir Bellare,et al.  Improved non-approximability results , 1994, STOC '94.

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

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

[5]  Luca Trevisan,et al.  Positive Linear Programming, Parallel Approximation and PCP's , 1996, ESA.

[6]  Osamu Watanabe,et al.  Randomized Approximation of the Constraint Satisfaction Problem , 1996, Nord. J. Comput..

[7]  Carsten Lund,et al.  Efficient probabilistically checkable proofs and applications to approximations , 1993, STOC.

[8]  Satissed Now Consider Improved Approximation Algorithms for Maximum Cut and Satissability Problems Using Semideenite Programming , 1997 .

[9]  Sanjeev Arora,et al.  Probabilistic checking of proofs: a new characterization of NP , 1998, JACM.

[10]  Johan Håstad,et al.  Some optimal inapproximability results , 1997, STOC '97.

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

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

[13]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.

[14]  Johan Håstad Testing of the long code and hardness for clique , 1996, STOC '96.

[15]  Rajeev Motwani,et al.  On syntactic versus computational views of approximability , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

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

[17]  Uriel Feige,et al.  Two prover protocols: low error at affordable rates , 1994, STOC '94.

[18]  David P. Williamson,et al.  A complete classification of the approximability of maximization problems derived from Boolean constraint satisfaction , 1997, STOC '97.

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

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

[21]  Luca Trevisan,et al.  MAX NP-Completeness Made Easy , 1999, Electron. Colloquium Comput. Complex..

[22]  Osamu Watanabe,et al.  Randomized Approximation of the Constraint Satisfaction Problem (Extended Abstract) , 1996, SWAT.

[23]  Nadia Creignou,et al.  A Dichotomy Theorem for Maximum Generalized Satisfiability Problems , 1995, J. Comput. Syst. Sci..

[24]  M. Bellare,et al.  Efficient probabilistic checkable proofs and applications to approximation , 1994, STOC '94.

[25]  Lars Engebretsen,et al.  Better Approximation Algorithms and Tighter Analysis for Set Splitting and Not-All-Equal Sat , 1997, Electron. Colloquium Comput. Complex..

[26]  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.