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:	https://eprints.sztaki.hu/id/eprint/7571

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