TY - JOUR

T1 - A 0.5-approximation algorithm for MAX DICUT with given sizes of parts

AU - Ageev, Alexander

AU - Hassin, Refael

AU - Sviridenko, Maxim

PY - 2001/2

Y1 - 2001/2

N2 - 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.

AB - 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.

KW - Approximation algorithm

KW - Basic solution

KW - Directed cut

KW - Linear relaxation

UR - http://www.scopus.com/inward/record.url?scp=0242564121&partnerID=8YFLogxK

U2 - 10.1137/S089548010036813X

DO - 10.1137/S089548010036813X

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AN - SCOPUS:0242564121

SN - 0895-4801

VL - 14

SP - 246

EP - 255

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 2

ER -