A 0.5-approximation algorithm for MAX DICUT with given sizes of parts

Alexander Ageev*, Refael Hassin, Maxim Sviridenko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given a directed graph G and an arc 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. Our main result is a 0.5-approximation algorithm for solving the problem. The algorithm is based on a tricky application of the pipage rounding technique developed in some earlier papers by two of the authors and a remarkable structural property of basic solutions to a linear relaxation. The property is that each component of any basic solution is an element of a set {0, δ, 1/2, 1 - δ, 1}, where δ is a constant that satisfies 0 < δ < 1/2 and is the same for all components.

Original languageEnglish
Pages (from-to)246-255
Number of pages10
JournalSIAM Journal on Discrete Mathematics
Issue number2
StatePublished - Feb 2001


  • Approximation algorithm
  • Basic solution
  • Directed cut
  • Linear relaxation


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