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.
Supported in part by the Russian Foundation for Basic Research, grant 99-01-00601.
Supported in part by the Russian Foundation for Basic Research, grant 99-01-00510.
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References
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© 2000 Springer-Verlag Berlin Heidelberg
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Ageev, A., Hassin, R., Sviridenko, M. (2000). An Approximation Algorithm for MAX DICUT with Given Sizes of Parts. In: Jansen, K., Khuller, S. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2000. Lecture Notes in Computer Science, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44436-X_5
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DOI: https://doi.org/10.1007/3-540-44436-X_5
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