A polynomial algebra method for computing exemplar breakpoint distance

Authors:
Bin Fu;Louxin Zhang
Affiliations:
Department of Computer Science, University of Texas-Pan American, Edinburg, TX;Department of Mathematics, National University of Singapore, Singapore
Venue:
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
Year:
2011

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Abstract

The exemplar breakpoint distance problem is NP-hard. Assume two genomes have at most n genes from m gene families. We develop an O(2mnO(1)) time algorithm to compute the exemplar breakpoint distance if one of them has no repetition. We develop an O(2mm!nO(1)) time algorithm to compute the exemplar breakpoint distance between two arbitrary genomes. If one of the given genomes has at most d repetitions for each gene, the computation time of the second algorithm is only O((2d)mnO(1)). Our algorithms are based on a polynomial algebra approach which uses a multilinear monomial to represent a solution for the exemplar breakpoint distance problem.