Complexity and approximation of satisfactory partition problems

Cristina Bazgan, Z. Tuza, Daniel Vanderpooten

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

The SATISFACTORY PARTITION problem consists of deciding if a given graph has a partition of its vertex set into two nonempty parts such that each vertex has at least as many neighbors in its part as in the other part. This problem was introduced by Gerber and Kobler in 1998 and further studied by other authors but its complexity remained open until now. We prove in this paper that SATISFACTORY PARTITION, as well as a variant where the parts are required to be of the same cardinality, are NP-complete. We also study approximation results for the latter problem, showing that it has no polynomial-time approximation scheme, whereas a constant approximation can be obtained in polynomial time. Similar results hold for balanced partitions where each vertex is required to have at most as many neighbors in its part as in the other part.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science
EditorsL. Wang
Pages829-838
Number of pages10
Volume3595
Publication statusPublished - 2005
Event11th Annual International Conference on Computing and Combinatorics, COCOON 2005 - Kunming, China
Duration: Aug 16 2005Aug 29 2005

Other

Other11th Annual International Conference on Computing and Combinatorics, COCOON 2005
CountryChina
CityKunming
Period8/16/058/29/05

Fingerprint

Partition
Polynomials
Approximation
Vertex of a graph
Polynomial Time Approximation Scheme
Cardinality
Polynomial time
NP-complete problem
Graph in graph theory

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Bazgan, C., Tuza, Z., & Vanderpooten, D. (2005). Complexity and approximation of satisfactory partition problems. In L. Wang (Ed.), Lecture Notes in Computer Science (Vol. 3595, pp. 829-838)

Complexity and approximation of satisfactory partition problems. / Bazgan, Cristina; Tuza, Z.; Vanderpooten, Daniel.

Lecture Notes in Computer Science. ed. / L. Wang. Vol. 3595 2005. p. 829-838.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bazgan, C, Tuza, Z & Vanderpooten, D 2005, Complexity and approximation of satisfactory partition problems. in L Wang (ed.), Lecture Notes in Computer Science. vol. 3595, pp. 829-838, 11th Annual International Conference on Computing and Combinatorics, COCOON 2005, Kunming, China, 8/16/05.
Bazgan C, Tuza Z, Vanderpooten D. Complexity and approximation of satisfactory partition problems. In Wang L, editor, Lecture Notes in Computer Science. Vol. 3595. 2005. p. 829-838
Bazgan, Cristina ; Tuza, Z. ; Vanderpooten, Daniel. / Complexity and approximation of satisfactory partition problems. Lecture Notes in Computer Science. editor / L. Wang. Vol. 3595 2005. pp. 829-838
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