A linear-time algorithm for the perfect phylogeny haplotype problem

The inference of evolutionary trees from binary species-character matrices is a fundamental computational problem in classical phylogenetic studies. Several problems arising in this field lead to different variants of the inference problem; some of these concern input data with missing values or incomplete matrices. A model of inference from incomplete data that has recently gained a remarkable interest is the Perfect Phylogeny Haplotype problem (PPH) introduced in [1] and successfully applied to infer haplotypes from genotype data. A stated open issue in this research field is the linear-time solution of this inference problem. In this paper we solve this question and give an 0(nm)-time algorithm to complete matrices of n rows and m columns to represent PPH solutions: we show that solving the problem requires recognizing special posets of width 2.