An approximation algorithm for MAX DICUT with given sizes of parts

  • Authors:

  • Alexander A. Ageev;Refael Hassin;Maxim Sviridenko

  • Affiliations:

  • -;-;-

  • Venue:
  • APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
  • Year:
  • 2000

  • 63-Approximation Algorithm for MAX DICUT

    APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization

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Abstract

Given a directed graph G and an edge weight function w : E(G) → R+, the maximum directed cut problem (max dicut) is that of finding a directed cut δ(X) with maximum total weight. In this paper we consider a version of MAX DICUT -- MAX DICUT with given sizes of parts or MAX DICUT WITH GSP -- whose instance is that of MAX DICUT plus a positive integer p, and it is required to find a directed cut δ(X) having maximum weight over all cuts δ(X) with |X| = p. It is known that by using semidefinite programming rounding techniques MAX DICUT can be well approximated -- the best approximation with a factor of 0.859 is due to Feige and Goemans. Unfortunately, no similar approach is known to be applicable to MAX DICUT WITH GSP. This paper presents an 0.5- approximation algorithm for solving the problem. The algorithm is based on exploiting structural properties of basic solutions to a linear relaxation in combination with the pipage rounding technique developed in some earlier papers by two of the authors.