Complexity and approximation of the Constrained Forest problem

Bazgan, Cristina and Couëtoux, Basile and Tuza, Zsolt (2011) Complexity and approximation of the Constrained Forest problem. THEORETICAL COMPUTER SCIENCE, 412 (32). pp. 4081-4091. ISSN 0304-3975

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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) [10]) but (2-1n)-approximable (Goemans and Williamson (1995) [9]). 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 O(lognloglogn) it has a ptas on planar graphs. © 2010 Elsevier B.V. All rights reserved.

Item Type: ISI Article
Uncontrolled Keywords: Treewidth, Planar graphs, Bipartite graphs, PTAS, Constrained Forest, APX-hardness, APPROXIMATION, COMPLEXITY
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: EPrints Admin
Date Deposited: 05 Feb 2014 12:16
Last Modified: 05 Feb 2014 15:47
URI: http://eprints.sztaki.hu/id/eprint/7571

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