Covering a graph with a constrained forest

Cristina Bazgan, Basile Couëtoux, Zsolt Tuza

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

1 Citation (Scopus)

Abstract

Given an undirected graph on n vertices with weights on its edges, Min WCF(p) consists of computing a covering forest of minimum weight such that each of its tree components contains at least p vertices. It has been proved that Min WCF(p) is NP-hard for any p≥4 (Imielinska et al., 1993) but -approximable (Goemans and Williamson, 1995). While Min WCF(2) is polynomial-time solvable, already the unweighted version of Min WCF(3) is NP-hard even on planar bipartite graphs of maximum degree 3. We prove here that for any p≥4, the unweighted version is NP-hard, even for planar bipartite graphs of maximum degree 3; moreover, the unweighted version for any p≥3 has no ptas for bipartite graphs of maximum degree 3. The latter theorem is the first-ever APX-hardness result on this problem. On the other hand, we show that Min WCF(p) is polynomial-time solvable on graphs with bounded treewidth, and for any p bounded by it has a ptas on planar graphs.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings
PublisherSpringer Verlag
Pages892-901
Number of pages10
ISBN (Print)3642106307, 9783642106309
DOIs
Publication statusPublished - Jan 1 2009
Event20th International Symposium on Algorithms and Computation, ISAAC 2009 - Honolulu, HI, United States
Duration: Dec 16 2009Dec 18 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5878 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other20th International Symposium on Algorithms and Computation, ISAAC 2009
CountryUnited States
CityHonolulu, HI
Period12/16/0912/18/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Bazgan, C., Couëtoux, B., & Tuza, Z. (2009). Covering a graph with a constrained forest. In Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings (pp. 892-901). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5878 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-10631-6_90