On cutting a few vertices from a graph

Uriel Feige, Robert Krauthgamer, Kobbi Nissim

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We consider the problem of finding in an undirected graph a minimum cut that separates exactly a given number k of vertices. For general k (i.e. k is part of the input and may depend on n) this problem is NP-hard. We present for this problem a randomized approximation algorithm, which is useful when k is relatively small. In particular, for k=O(log n) we obtain a polynomial time approximation scheme, and for k=Ω(log n) we obtain an approximation ratio O(k/log n).

Original languageEnglish
Pages (from-to)643-649
Number of pages7
JournalDiscrete Applied Mathematics
Issue number3
StatePublished - 1 May 2003
Externally publishedYes


  • Approximation algorithms
  • Dynamic programming
  • Graph partitioning
  • Random edge contraction

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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