Analysis on the complexity of the problem to construct the most parsimonious phylogenetic trees

With the availability of ever-increasing gene sequence data across a large number of species, reconstruction of phylogenetic trees to reveal the evolution relationship among those species becomes more and more important. In this paper, we present a novel proof of the NP-completeness of the large parsimony problem by reduction from a newly-proved NP-complete problem to gain additional insight of this fundamental problem in computational biology. We then conduct experiments based upon our recent work of a random tree optimization algorithm based on cross-entropy method for the construction of the most parsimonious phylogenetic trees across 12 Drosophila genomes.