An Approximation Algorithm for MAX DICUT with Given Sizes of Parts
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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- 1.A.A. Ageev and M.I. Sviridenko, Approximation algorithms for Maximum Coverage and Max Cut with given sizes of parts, Lecture Notes in Computer Science (Proceedings of IPCO’99) 1610 (1999), 17–30.Google Scholar
- 2.A.A. Ageev and M.I. Sviridenko, An approximation algorithm for Hypergraph Max k-Cut with given sizes of parts, Lecture Notes in Computer Science (Proceedings of ESA’2000), to appear.Google Scholar
- 3.U. Feige and M.X. Goemans, Approximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT, Proceedings of the Third Israel Symposium on Theory of Computing and Systems (1995), 182–189.Google Scholar
- 4.U. Feige and M. Langberg, Approximation algorithms for maximization problems arising in graph partitioning, manuscript, 1999.Google Scholar
- 6.K. Jain, A factor 2 approximation algorithm for the generalized Steiner network problem, Proceedings of FOCS’98 (1998), 448–457.Google Scholar
- 7.V. Melkonian and É. Tardos, Approximation algorithms for a directed network design problem, Lecture Notes in Computer Science (Proceedings of IPCO’99) 1610 (1999), 345–360.Google Scholar