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 -