On approximation algorithms for local multiple alignment

Authors:
Tatsuya Akutsu;Hiroki Arimura;Shinichi Shimozono
Affiliations:
Human Genome Center, Institute of Medical Science, University of Tokyo, 4-6-1 Shirokanedai, Minato-ku, Tokyo 108-8639, Japan;Graduate School of Information Science, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan;Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka-city, Fukuoka 820-8502, Japan
Venue:
RECOMB '00 Proceedings of the fourth annual international conference on Computational molecular biology
Year:
2000

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Abstract

This paper studies the local multiple alignment problem, which is also known as the general consensus patterns problem. Local multiple alignment is, given protein or DNA sequences, to locate a region (i.e., a substring) of fixed length from each sequence so that the score determined from the set of regions is optimized. We consider the following scoring schemes. the score indicating the average information content, the score defined by Li et al, and the sum-of-pairs scoreWe prove that multiple local alignment is NP-hard under each of these scoring schemes. In addition, we prove that multiple local alignment is APX-hard under the average information content scoring. It implies that unless P = NP there is no polynomial time algorithm whose worst case approximation error can be arbitrarily specified (precisely, a polynomial time approximation scheme). Several related theoretical results are provided.We also made computational experiments on approximation algorithms for local multiple alignment under the average information content scoring. The results suggest that the Gibbs sampling algorithm proposed by Lawrence et al. is the best.