Approximation algorithms for maximum cut with limited unbalance

We consider the problem of partitioning the vertices of a weighted graph into two sets of sizes that differ at most by a given threshold B , so as to maximize the weight of the crossing edges. For B equal to 0 this problem is known as Max Bisection, whereas for B equal to the number n of nodes it is...

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Bibliographic Details
Published in:Theoretical computer science Vol. 385; no. 1; pp. 78 - 87
Main Authors: Galbiati, Giulia, Maffioli, Francesco
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 15.10.2007
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Approximations and expansions
Computer science; control theory; systems
Exact sciences and technology
Information retrieval. Graph
Limited unbalance cut
Mathematical analysis
Mathematics
Maximum cut
Miscellaneous
Randomized approximation algorithm
Sciences and techniques of general use
Semidefinite programming
Theoretical computing
Randomized approximation algorithm
Maximum cut
Semidefinite programming
Limited unbalance cut
Polynomial
Computer theory
Methodology
Polynomial approximation
Node
Semi definite programming
Approximation algorithm
Weighted graph
Polynomial time
Maximum
Performance
Threshold
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:We consider the problem of partitioning the vertices of a weighted graph into two sets of sizes that differ at most by a given threshold B , so as to maximize the weight of the crossing edges. For B equal to 0 this problem is known as Max Bisection, whereas for B equal to the number n of nodes it is the maximum cut problem. We present polynomial time randomized approximation algorithms with non trivial performance guarantees for its solution. The approximation results are obtained by extending the methodology used by Y. Ye for Max Bisection and by combining this technique with another one that uses the algorithm of Goemans and Williamson for the maximum cut problem. When B is equal to zero the approximation ratio achieved coincides with the one obtained by Y. Ye; otherwise it is always above this value and tends to the value obtained by Goemans and Williamson as B approaches the number n of nodes.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2007.05.036