Approximation of satisfactory bisection problems

Cristina Bazgan, Zsolt Tuza, Daniel Vanderpooten

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The Satisfactory Bisection problem means to decide whether a given graph has a partition of its vertex set into two parts of the same cardinality such that each vertex has at least as many neighbors in its part as in the other part. A related variant of this problem, called Co-Satisfactory Bisection, requires that each vertex has at most as many neighbors in its part as in the other part. A vertex satisfying the degree constraint above in a partition is called 'satisfied' or 'co-satisfied,' respectively. After stating the NP-completeness of both problems, we study approximation results in two directions. We prove that maximizing the number of (co-)satisfied vertices in a bisection has no polynomial-time approximation scheme (unless P = NP), whereas constant approximation algorithms can be obtained in polynomial time. Moreover, minimizing the difference of the cardinalities of vertex classes in a bipartition that (co-)satisfies all vertices has no polynomial-time approximation scheme either.

Original languageEnglish
Pages (from-to)875-883
Number of pages9
JournalJournal of Computer and System Sciences
Volume74
Issue number5
DOIs
Publication statusPublished - Aug 2008

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Keywords

  • Approximation algorithm
  • Complexity
  • Degree constraints
  • Graph
  • NP-complete
  • Vertex partition

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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