On cutting a few vertices from a graph

Authors:
Uriel Feige;Robert Krauthgamer;Kobbi Nissim
Affiliations:
Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel;International Computer Science Institute, 1947 Center Street, Suite 600, Berkeley, CA and Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Isra ...;DIMACS Center, 96 Frelinghuysen Rd., Piscataway, NJ
Venue:
Discrete Applied Mathematics
Year:
2003

Citing 5
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Abstract

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).