On cutting a few vertices from a graph

Uriel Feige; Robert Krauthgamer; Kobbi Nissim

doi:10.1016/S0166-218X(02)00394-3

On cutting a few vertices from a graph

Uriel Feige, Robert Krauthgamer, Kobbi Nissim

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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).

Original language	English
Pages (from-to)	643-649
Number of pages	7
Journal	Discrete Applied Mathematics
Volume	127
Issue number	3
DOIs	https://doi.org/10.1016/S0166-218X(02)00394-3
State	Published - 1 May 2003
Externally published	Yes

Keywords

Approximation algorithms
Dynamic programming
Graph partitioning
Random edge contraction

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/S0166-218X(02)00394-3

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AU - Feige, Uriel

AU - Krauthgamer, Robert

AU - Nissim, Kobbi

N1 - Funding Information: This research was supported in part by a Minerva grant.

PY - 2003/5/1

Y1 - 2003/5/1

N2 - 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).

AB - 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).

KW - Approximation algorithms

KW - Dynamic programming

KW - Graph partitioning

KW - Random edge contraction

UR - https://www.scopus.com/pages/publications/84867951886

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M3 - Article

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SP - 643

EP - 649

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 3

ER -

On cutting a few vertices from a graph

Abstract

Keywords

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