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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Vydané v:	Theoretical computer science Ročník 385; číslo 1; s. 78 - 87
Hlavní autori:	Galbiati, Giulia, Maffioli, Francesco
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 15.10.2007 Elsevier
Predmet:	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
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Abstract	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.
AbstractList	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.
Author	Maffioli, Francesco Galbiati, Giulia
Author_xml	– sequence: 1 givenname: Giulia surname: Galbiati fullname: Galbiati, Giulia email: giulia.galbiati@unipv.it organization: Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia, 27100 Pavia, Italy – sequence: 2 givenname: Francesco surname: Maffioli fullname: Maffioli, Francesco email: maffioli@elet.polimi.it organization: Dipartimento di Elettronica e Informazione, Politecnico di Milano, 20133 Milano, Italy
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Keywords	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
Language	English
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SubjectTerms	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
Title	Approximation algorithms for maximum cut with limited unbalance
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