Simple Approximation Algorithms for Balanced MAX 2SAT

  • Alice Paul
  • Matthias PoloczekEmail author
  • David P. Williamson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)


We study simple algorithms for the balanced MAX 2SAT problem, where we are given weighted clauses of length one and two with the property that for each variable x the total weight of clauses that x appears in equals the total weight of clauses for \(\overline{x}\). We show that such instances have a simple structural property in that any optimal solution can satisfy at most the total weight of the clauses minus half the total weight of the unit clauses. Using this property, we are able to show that a large class of greedy algorithms, including Johnson’s algorithm, gives a \(\frac{3}{4}\)-approximation algorithm for balanced MAX 2SAT; a similar statement is false for general MAX 2SAT instances. We further give a spectral 0.81-approximation algorithm for balanced MAX E2SAT instances (in which each clause has exactly 2 literals) by a reduction to a spectral algorithm of Trevisan for the maximum colored cut problem. We provide experimental results showing that this spectral algorithm performs well and is slightly better than Johnson’s algorithm and the Goemans-Williamson semidefinite programming algorithm on balanced MAX E2SAT instances.


Approximation Algorithm Greedy Algorithm Approximation Ratio Semidefinite Programming Performance Guarantee 
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Supplementary material


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Alice Paul
    • 1
  • Matthias Poloczek
    • 1
    Email author
  • David P. Williamson
    • 1
  1. 1.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

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