Approximation Algorithm for Non-boolean MAX k-CSP

  • Konstantin Makarychev
  • Yury Makarychev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7408)

Abstract

In this paper, we present a randomized polynomial-time approximation algorithm for MAX k-CSP d . In MAX k-CSP d , we are given a set of predicates of arity k over an alphabet of size d. Our goal is to find an assignment that maximizes the number of satisfied constraints.

Our algorithm has approximation factor Ω(kd/d k ) (when k ≥ Ω(logd)). This bound is asymptotically optimal assuming the Unique Games Conjecture. The best previously known algorithm has approximation factor Ω(klogd/d k ).

We also give an approximation algorithm for the boolean MAX k-CSP2 problem with a slightly improved approximation guarantee.

Keywords

Approximation Algorithm Constraint Satisfaction Problem Approximation Factor Random Gaussian Vector Inapproximability Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Konstantin Makarychev
    • 1
  • Yury Makarychev
    • 2
  1. 1.Microsoft ResearchUSA
  2. 2.Toyota Technological Institute at ChicagoUSA

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