Algorithmica

, Volume 27, Issue 2, pp 198–207

Approximation Algorithms for Minimum K -Cut

  • N. Guttmann-Beck
  • R. Hassin

DOI: 10.1007/s004530010013

Cite this article as:
Guttmann-Beck, N. & Hassin, R. Algorithmica (2000) 27: 198. doi:10.1007/s004530010013

Abstract.

Let G=(V,E) be a complete undirected graph, with node set V={v1, . . ., vn } and edge set E . The edges (vi,vj) ∈ E have nonnegative weights that satisfy the triangle inequality. Given a set of integers K = { ki }i=1p\((\sum_{i=1}^p k_i \leq |V|\) , the minimum K-cut problem is to compute disjoint subsets with sizes { ki }i=1p , 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.

Key words. Approximation algorithms, Minimum cuts.

Copyright information

© 2000 Springer-Verlag New York Inc.

Authors and Affiliations

  • N. Guttmann-Beck
    • 1
  • R. Hassin
    • 1
  1. 1.Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv 69978, Israel. nili@math.tau.ac.il, hassin@math.tau.ac.il. IL