Approximation algorithms for MAX RES CUT with limited unbalanced constraints

Two kinds of MAX RES CUT problems, the MAX s − t CUT and the MAX s − t − v CUT, with limited unbalanced constraints are considered. Approximation algorithms used in Frieze and Jerrum (Integer Programming and Combinatorial Optimization, vol. 920, pp. 1–13, Springer, Berlin, 1995 ), Galbiati and Maffi...

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Veröffentlicht in:Journal of applied mathematics & computing Jg. 33; H. 1-2; S. 357 - 374
Hauptverfasser: Ling, Aifan, Tang, Le, Xu, Chengxian
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer-Verlag 01.06.2010
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Computer programming
Graphs
Integer programming
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Random variables
Studies
Theory of Computation
Theory of constraints
90C35
Limited unbalanced constraints
Semidefinite programming relaxation
90C06
90C59
90C27
Approximation algorithm
MAX RES CUT
ISSN:1598-5865, 1865-2085
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Zusammenfassung:Two kinds of MAX RES CUT problems, the MAX s − t CUT and the MAX s − t − v CUT, with limited unbalanced constraints are considered. Approximation algorithms used in Frieze and Jerrum (Integer Programming and Combinatorial Optimization, vol. 920, pp. 1–13, Springer, Berlin, 1995 ), Galbiati and Maffioli (Theor. Comput. Sci. 385:78–87, 2007 ), Han et al. (Math. Program. Ser. B 92:509–535, 2002 ) and Ye (Math. Programm. 90:101–111, 2001 ) are extended to the two MAX RES CUT problems. A special matrix P is constructed by which it can ensure that the given nodes s , t are feasible to equality constraints with probability one for the MAX s − t CUT and s , t , v are feasible to equality constraints with at least probability 0.912 for the MAX s − t − v CUT. A fussy greedy sizing-adjusted procedure is then proposed to confirm that the round solution is feasible for all constraints. We find these extensions are nontrivial and some interesting results about performance ratio are obtained for the MAX RES CUT problem with limited unbalanced constraints.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-009-0290-1