, Volume 27, Issue 2, pp 198207
First online:
Approximation Algorithms for Minimum K Cut
 N. GuttmannBeckAffiliated withDepartment of Statistics and Operations Research, Tel Aviv University, Tel Aviv 69978, Israel. nili@math.tau.ac.il, hassin@math.tau.ac.il.
 , R. HassinAffiliated withDepartment of Statistics and Operations Research, Tel Aviv University, Tel Aviv 69978, Israel. nili@math.tau.ac.il, hassin@math.tau.ac.il.
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Let G=(V,E) be a complete undirected graph, with node set V={v _{ 1 } , . . ., v _{ n } } and edge set E . The edges (v _{ i } ,v _{ j } ) ∈ E have nonnegative weights that satisfy the triangle inequality. Given a set of integers K = { k _{ i } } _{ i=1 } ^{ p } \((\sum_{i=1}^p k_i \leq V\) , the minimum Kcut problem is to compute disjoint subsets with sizes { k _{ i } } _{ i=1 } ^{ p } , minimizing the total weight of edges whose two ends are in different subsets. We demonstrate that for any fixed p it is possible to obtain in polynomial time an approximation of at most three times the optimal value. We also prove bounds on the ratio between the weights of maximum and minimum cuts.
 Title
 Approximation Algorithms for Minimum K Cut
 Journal

Algorithmica
Volume 27, Issue 2 , pp 198207
 Cover Date
 200006
 DOI
 10.1007/s004530010013
 Print ISSN
 01784617
 Online ISSN
 14320541
 Publisher
 SpringerVerlag
 Additional Links
 Keywords

 Key words. Approximation algorithms, Minimum cuts.
 Industry Sectors
 Authors

 N. GuttmannBeck ^{(A1)}
 R. Hassin ^{(A1)}
 Author Affiliations

 A1. Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv 69978, Israel. nili@math.tau.ac.il, hassin@math.tau.ac.il., IL