The Worst Case Complexity of Maximum Parsimony

Abstract

One of the core classical problems in computational biology is that of constructing the most parsimonious phylogenetic tree interpreting an input set of sequences from the genomes of evolutionarily related organisms. We reexamine the classical maximum parsimony (MP) optimization problem for the general (asymmetric) scoring matrix case, where rooted phylogenies are implied, and analyze the worst case bounds of three approaches to MP: The approach of Cavalli-Sforza and Edwards, the approach of Hendy and Penny, and a new agglomerative, ''bottom-up'' approach we present in this article. We show that the second and third approaches are faster than the first one by a factor of Y( ffiffiffi n p ) and H(n), respectively, where n is the number of species.

Live phylogeny with polytomies: Finding the most compact parsimonious trees

“…Some previous work in polytomies focused on constant time heuristic improvements [17]; our work instead focuses on native methods for identifying the most parsimonious tree allowing for polytomies. Lack of work in this area may be a result of the additional complexity polytomies add to an already hard computational problem [18], [19], [20], [21].…”