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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 evolutionary tree, a well-known biologically-motivated data structure. For PH we extend recent work of [17] by further mapping the interface between “easy” and “hard” instances, within the framework of (k,l)-bounded instances. By exploring, in the same way, the tractability frontier of MPPH we provide the first concrete, positive results for this problem, and the algorithms underpinning these results offer new insights about how MPPH might be further tackled in the future. In both PH and MPPH intriguing open problems remain.

Beaches of Islands of Tractability: Algorithms for Parsimony and Minimum Perfect Phylogeny Haplotyping Problems