A Decomposition of the Pure Parsimony Haplotyping Problem

Authors:
Allen Holder;Thomas Langley
Affiliations:
Rose-Hulman Institute of Technology, Terre Haute, IN 47803;Rose-Hulman Institute of Technology, Terre Haute, IN 47803
Venue:
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
Year:
2009

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Abstract

We partially order a collection of genotypes so that we can represent the NP-Hard problem of inferring the least number of haplotypes in terms of substructures we call g-lattices. This representation allows us to prove that the problem can be solved efficiently if the genotypes partition into chains with certain structure. Even without the specified structure, the decomposition shows how to separate the underlying integer programming model into smaller models.