Simpler 3/4-Approximation Algorithms for MAX SAT
نویسنده
چکیده
We consider the recent randomized 3 4 -algorithm for MAX SAT of Poloczek and Schnitger. We give a much simpler set of probabilities for setting the variables to true or false, which achieve the same expected performance guarantee. Our algorithm suggests a conceptually simple way to get a deterministic algorithm: rather than comparing to an unknown optimal solution, we instead compare the algorithm’s output to the optimal solution of an LP relaxation. This gives rise to a new LP rounding algorithm, which also achieves a performance guarantee of 3 4 .
منابع مشابه
On Some Recent MAX SAT Approximation Algorithms
Recently a number of randomized 3 4 -approximation algorithms for MAX SAT have been proposed that all work in the same way: given a fixed ordering of the variables, the algorithm makes a random assignment to each variable in sequence, in which the probability of assigning each variable true or false depends on the current set of satisfied (or unsatisfied) clauses. To our knowledge, the first su...
متن کاملBounds on Greedy Algorithms for MAX SAT
We study adaptive priority algorithms for MAX SAT and show that no such deterministic algorithm can reach approximation ratio 3 4 , assuming an appropriate model of data items. As a consequence we obtain that the Slack–Algorithm of [13] cannot be derandomized. Moreover, we present a significantly simpler version of the Slack–Algorithm and also simplify its analysis. Additionally, we show that t...
متن کاملApproximation algorithms for MAX 4 - SATand rounding procedures for semide nite programs
Karloo 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 semideenite programming relaxation of MAX 4-SAT and a new family of rounding procedures that try to cope well...
متن کاملOn Approximation Algorithms for Hierarchical MAX-SAT
We prove upper and lower bounds on performance guarantees of approximation algorithms for the Hierarchical MAX-SAT (H-MAX-SAT) problem. This problem is representative of a broad class of PSPACE-hard problems involving graphs, Boolean formulas and other structures that are de ned succinctly. Our rst result is that for some constant < 1, it is PSPACE-hard to approximate the function H-MAX-SAT to ...
متن کاملApproximation Algorithms for MAX 4-SAT and Rounding Procedures for Semidefinite Programs
Karloo 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 semideenite programming relaxation of MAX 4-SAT and a new family of rounding procedures that try to cope well...
متن کامل