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.


Approximation Algorithm Constraint Satisfaction Problem Approximation Factor Random Gaussian Vector Inapproximability Result 
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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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