Finding good approximate vertex and edge partitions is NP-hard

Thang Nguyen Bui, Curt Jones

Research output: Contribution to journalArticlepeer-review

197 Scopus citations

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

All Science Journal Classification (ASJC) codes

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

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