Efficient Computation of Template Matrices

The computation of template matrices is the bottleneck of simple algorithms for perfect phylogeny haplotyping and for perfect phylogeny under mutation and constrained recombination. The fastest algorithms known so far compute them in O(nm) time. In this paper, we describe an algorithm for computing template matrices in O(nm/ log(n)) time. We also present and discuss a conjecture that implies an O(nm+m) time algorithm for computing them and, as a consequence, O(nm + m) time simple solutions to the perfect phylogeny haplotyping problem and to the perfect phylogeny problem under mutation and constrained recombination, as well as an O(n) time solution to the boolean matrix multiplication problem.