Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
On the approximation of maximum satisfiability
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
New ${\bf \frac{3}{4}}$-Approximation Algorithms for the Maximum Satisfiability Problem
SIAM Journal on Discrete Mathematics
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Finding almost-satisfying assignments
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Approximating Satisfiable Satisfiability Problems (Extended Abstract)
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Approximation algorithms for the maximum satisfiability problem
Nordic Journal of Computing
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximation Algorithms for MAX SAT: Yannakakis vs. Goemans-Williamson
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
Gadgets Approximation, and Linear Programming
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
On syntactic versus computational views of approximability
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Hi-index | 0.00 |
Karloff and Zwick obtained recently an optimal 7/8-approximation algorithm for MAX 3-SAT. In an attempt to see whether similar methods can be used to obtain a 7/8-approximation algorithm for MAX SAT, we consider the most natural generalization of MAX 3-SAT, namely MAX 4-SAT. We present a semidefinite programming relaxation of MAX 4-SAT and a new family of rounding procedures that try to cope well with clauses of various sizes. We study the potential, and the limitations, of the relaxation and of the proposed family of rounding procedures using a combination of theoretical and experimental means. We select two rounding procedures from the proposed family of rounding procedures. Using the first rounding procedure we seem to obtain an almost optimal 0:8721-approximation algorithm for MAX 4-SAT. Using the second rounding procedure we seem to obtain an optimal 7/8-approximation algorithm for satisfiable instances of MAX 4-SAT. On the other hand, we show that no rounding procedure from the family considered can yield an approximation algorithm for MAX 4-SAT whose performance guarantee on all instances of the problem is greater than 0.8724. Although most of this paper deals specifically with the MAX 4-SAT problem, we believe that the new family of rounding procedures introduced, and the methodology used in the design and in the analysis of the various rounding procedures considered would have a much wider range of applicability.