New ${\bf \frac{3}{4}}$-Approximation Algorithms for the Maximum Satisfiability Problem

  • Authors:
  • Michel X. Goemans;David P. Williamson

  • Affiliations:
  • -;-

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 1994

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Abstract

Yannakakis recently presented the first $\frac{3}{4}$-approximation algorithm for the Maximum Satisfiability Problem (MAX SAT). His algorithm makes nontrivial use of solutions to maximum flow problems. New, simple $\frac{3}{4}$-approximation algorithms that apply the probabilistic method/randomized rounding to the solution to a linear programming relaxation of MAX SAT are presented. It is shown that although standard randomized rounding does not give a good approximate result, the best solution of the two given by randomized rounding and a well-known algorithm of Johnson is always within $\frac{3}{4}$ of the optimal solution. It is further shown that an unusual twist on randomized rounding also yields $\frac{3}{4}$-approximation algorithms. As a by-product of the analysis, a tight worst-case analysis of the relative duality gap of the linear programming relaxation is obtained.