Finding good approximate vertex and edge partitions is NP-hard

Thang Nguyen Bui, Curt Jones

Research output: Contribution to journalArticle

186 Citations (Scopus)

Abstract

In this paper we show that for n-vertex graphs with maximum degree 3, and for any fixed ε> 0, it is NP-hard to find α-edge separators and α-vertex separators of size no more than OPT+n 1 2 - ε, where OPT is the size of the optimal solutio n. For general graphs we show that it is NP-hard to find an α-edge separator of size no more than OPT+n2 - ε. We also show that an O(f{hook}(n))-approximation algorithm for finding α-vertex separators of maximum degree 3 graphs can be used to find an O(f{hook}(n5))-approximation algorithm for finding α-edge separators of general graphs. Since it is NP-hard to find optimal α-edge separators for general graphs this means that it is NP-hard to find optimal vertex separators even when restricted to maximum degree 3 graphs.

Original languageEnglish (US)
Pages (from-to)153-159
Number of pages7
JournalInformation Processing Letters
Volume42
Issue number3
DOIs
StatePublished - May 25 1992

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Separator
Separators
NP-complete problem
Partition
Vertex of a graph
Graph in graph theory
Maximum Degree
Approximation algorithms
Approximation Algorithms

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

Cite this

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title = "Finding good approximate vertex and edge partitions is NP-hard",
abstract = "In this paper we show that for n-vertex graphs with maximum degree 3, and for any fixed ε> 0, it is NP-hard to find α-edge separators and α-vertex separators of size no more than OPT+n 1 2 - ε, where OPT is the size of the optimal solutio n. For general graphs we show that it is NP-hard to find an α-edge separator of size no more than OPT+n2 - ε. We also show that an O(f{hook}(n))-approximation algorithm for finding α-vertex separators of maximum degree 3 graphs can be used to find an O(f{hook}(n5))-approximation algorithm for finding α-edge separators of general graphs. Since it is NP-hard to find optimal α-edge separators for general graphs this means that it is NP-hard to find optimal vertex separators even when restricted to maximum degree 3 graphs.",
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Finding good approximate vertex and edge partitions is NP-hard. / Bui, Thang Nguyen; Jones, Curt.

In: Information Processing Letters, Vol. 42, No. 3, 25.05.1992, p. 153-159.

Research output: Contribution to journalArticle

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