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An Integer Programming Formulation of the Parsimonious Loss of Heterozygosity Problem
Nov.-Dec. 2013 (vol. 10 no. 6)
pp. 1391-1402
Daniele Catanzaro, Université Libre de Bruxelles (ULB), Brussels
Martine Labbe, Université Libre de Bruxelles (ULB), Brussels
Bjarni V. Halldorsson, Reykjavik University, Reykjavik
A loss of heterozygosity (LOH) event occurs when, by the laws of Mendelian inheritance, an individual should be heterozygote at a given site but, due to a deletion polymorphism, is not. Deletions play an important role in human disease and their detection could provide fundamental insights for the development of new diagnostics and treatments. In this paper, we investigate the parsimonious loss of heterozygosity problem (PLOHP), i.e., the problem of partitioning suspected polymorphisms from a set of individuals into a minimum number of deletion areas. Specifically, we generalize Halldórsson et al.'s work by providing a more general formulation of the PLOHP and by showing how one can incorporate different recombination rates and prior knowledge about the locations of deletions. Moreover, we show that the PLOHP can be formulated as a specific version of the clique partition problem in a particular class of graphs called undirected catch-point interval graphs and we prove its general $({\cal NP})$-hardness. Finally, we provide a state-of-the-art integer programming (IP) formulation and strengthening valid inequalities to exactly solve real instances of the PLOHP containing up to 9,000 individuals and 3,000 SNPs. Our results give perspectives on the mathematics of the PLOHP and suggest new directions on the development of future efficient exact solution approaches.
Index Terms:
Bioinformatics,Genomics,DNA,Human factors,Computational biology,Linear programming,single nucleotide polymorphism,Clique partitioning,submodular functions,polymatroid rank functions,undirected catch-point interval graph,combinatorial optimization,mixed integer programming,computational biology,loss of heterozygosity,genome-wide association studies
Daniele Catanzaro, Martine Labbe, Bjarni V. Halldorsson, "An Integer Programming Formulation of the Parsimonious Loss of Heterozygosity Problem," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 6, pp. 1391-1402, Nov.-Dec. 2013, doi:10.1109/TCBB.2012.138
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