An Approximation Algorithm for MAX DICUT with Given Sizes of Parts

  • Alexander Ageev
  • Refael Hassin
  • Maxim Sviridenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1913)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Alexander Ageev
    • 1
  • Refael Hassin
    • 2
  • Maxim Sviridenko
    • 3
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.School of Mathematical SciencesTel Aviv UniversityIsrael
  3. 3.BRICS University of AarhusAarhusDenmark

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