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 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.