Some approximation algorithms for the clique partition problem in weighted interval graphs

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)124-133
Journal / PublicationTheoretical Computer Science
Volume381
Issue number1-3
Publication statusPublished - 22 Aug 2007

Abstract

Interval graphs play important roles in analysis of DNA chains in Benzer [S. Benzer, On the topology of the genetic fine structure, Proceedings of the National Academy of Sciences of the United States of America 45 (1959) 1607-1620], restriction maps of DNA in Waterman and Griggs [M.S. Waterman, J.R. Griggs, Interval graphs and maps of DNA, Bulletin of Mathematical Biology 48 (2) (1986) 189-195] and other related areas. In this paper, we study a new combinatorial optimization problem, named the minimum clique partition problem with constrained bounds, in weighted interval graphs. For a weighted interval graph G and a bound B, partition the weighted intervals of this graph G into the smallest number of cliques, such that each clique, consisting of some intervals whose intersection on a real line is not empty, has its weight not beyond B. We obtain the following results: (1) this problem is NP-hard in a strong sense, and it cannot be approximated within a factor frac(3, 2) - ε in polynomial time for any ε > 0; (2) we design three approximation algorithms with different constant factors for this problem; (3) for the version where all intervals have the same weights, we design an optimal algorithm to solve the problem in linear time. © 2007 Elsevier Ltd. All rights reserved.

Research Area(s)

  • Approximation algorithms, Cliques, Weighted interval graphs

Citation Format(s)

Some approximation algorithms for the clique partition problem in weighted interval graphs. / Chen, Mingxia; Li, Jianbo; Li, Jianping et al.
In: Theoretical Computer Science, Vol. 381, No. 1-3, 22.08.2007, p. 124-133.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review