The Three-state Perfect Phylogeny Problem Reduces to 2-SAT

Abstract

We extend a structural result by A. Dress and M. Steel, "Convex tree realizations of partitions," Applied Math Letters, 5 (1993), pp. 3–6., to show that the three-state Perfect Phylogeny problem reduces in polynomial time to the classic 2-SAT problem. We also give a more expanded exposition of the proof of the structural result from Dress and Steel. We hope this note will encourage additional researchers to try to solve the central open question: finding simple efficient solutions to the k-state Perfect Phylogeny problem for k > 3.