Tight bound on Johnson's algorithm for Max-SAT

We present a new technique that gives a more thorough analysis on Johnson's classical algorithm for the maximum satisfiability problem. In contrast to the common belief for two decades that Johnson's algorithm has performance ratio 1/2, we show that the performance ratio is 2/3, and that this bound is tight. Moreover we show that simple generalizations of Johnson's algorithm do not improve the performance ratio bound 2/3.

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

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

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

[4]  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.

[5]  Jianer Chen,et al.  Tight Bound on Johnson's Algorithm for Maximum Satisfiability , 1999, J. Comput. Syst. Sci..

[6]  Karl J. Lieberherr,et al.  Complexity of partial satisfaction , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

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

[8]  Ramesh Hariharan,et al.  Derandomizing semidefinite programming based approximation algorithms , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

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

[10]  Luca Trevisan,et al.  Gadgets, approximation, and linear programming , 1996, Proceedings of 37th Conference on Foundations of Computer Science.