title: Shorelines of islands of tractability: algorithms for parsimony and minimum perfect phylogeny haplotyping problems.
abstract: 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.
authors.affiliation: Technische Universiteit Eindhoven, Eindhoven, The Netherlands. l.j.j.v.iersel@tue.nl
authors.forename: Leo
authors.initials: L
authors.lastname: van Iersel
authors.forename: Judith
authors.initials: J
authors.lastname: Keijsper
authors.forename: Steven
authors.initials: S
authors.lastname: Kelk
authors.forename: Leen
authors.initials: L
authors.lastname: Stougie
mesh_terms: D000465:Algorithms; D005075:Biological Evolution; D019295:Computational Biology; D005838:Genotype; D006239:Haplotypes; D008957:Models, Genetic; D015233:Models, Statistical; D010802:Phylogeny