On the advantage over a random assignment

  • Authors:

  • Johan Håstad;S. Venkatesh

  • Affiliations:

  • Nada, KTH, SE-100 44 Stockholm, Sweden;DIMACS Center, CoRE Building, Rutgers University, 96 Frelinghuysen Road, Piscataway, New Jersey

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2004

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Abstract

We initiate the study of a new measure of approximation. This measure compares the performance of an approximation algorithm to the random assignment algorithm. This is a useful measure for optimization problems where the random assignment algorithm is known to give essentially the best possible polynomial time approximation. In this paper, we focus on this measure for the optimization problems Max-Lin-2 in which we need to maximize the number of satisfied linear equations in a system of linear equations modulo 2, and Max-k-Lin-2, a special case of the above problem in which each equation has at most k variables. The main techniques we use, in our approximation algorithms and inapproximability results for this measure, are from Fourier analysis and derandomization.