Shorelines of islands of tractability: algorithms for parsimony and minimum perfect phylogeny haplotyping problems.

IEEE/ACM transactions on computational biology and bioinformatics / IEEE, ACM

PubMedID: 18451439

van Iersel L, Keijsper J, Kelk S, Stougie L. Shorelines of islands of tractability: algorithms for parsimony and minimum perfect phylogeny haplotyping problems. IEEE/ACM Trans Comput Biol Bioinform. 2008;5(2):301-12.
The problem Parsimony Haplotyping (PH) asks for the smallest set of haplotypes which can explain a given set of genotypes, and the problem Minimum Perfect Phylogeny Haplotyping (MPPH) asks for the smallest such set which also allows the haplotypes to be embedded in a perfect phylogeny, an evolutionary tree with biologically-motivated restrictions. For PH, we extend recent work by further mapping the interface between ;;easy'' and ;;hard'' instances, within the framework of (k,l)-bounded instances where the number of 2's per column and row of the input matrix is restricted. By exploring, in the same way, the tractability frontier of MPPH we provide the first concrete, positive results for this problem. In addition, we construct for both PH and MPPH polynomial time approximation algorithms, based on properties of the columns of the input matrix.