Decompositions of Multiple Breakpoint Graphs and Rapid Exact Solutions to the Median Problem

Authors:
Andrew Wei Xu;David Sankoff
Affiliations:
Department of Mathematics and Statistics, University of Ottawa, Canada K1N 6N5;Department of Mathematics and Statistics, University of Ottawa, Canada K1N 6N5
Venue:
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Year:
2008

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Abstract

The median genome problem reduces to a search for the vertex matching in the multiple breakpoint graph (MBG) that maximizes the number of alternating colour cycles formed with the matchings representing the given genomes. We describe a class of "adequate" subgraphs of MBGs that allow a decomposition of an MBG into smaller, more easily solved graphs. We enumerate all of these graphs up to a certain size and incorporate the search for them into an exhaustive algorithm for the median problem. This enables a dramatic speedup in most randomly generated instances with hundreds or even thousands of vertices, as long as the ratio of genome rearrangements to genome size is not too large.