2014/12/12 by Steven Kelk, Mareike Fischer, Kelk, Steven +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Earth and Planetary Sciences · Mathematics · #05C15 #05C35 #90C35 #92D15 #Combinatorics (math.CO) #Computational Engineering #Data Structures and Algorithms (cs.DS) #Evolution and Paleontology Studies #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Finance #Genetic diversity and population structure #Genomics and Phylogenetic Studies #Populations and Evolution (q-bio.PE) #and Science (cs.CE) #cs.CE #cs.DS #math.CO #msc:05C15 #msc:05C35 #msc:90C35 #msc:92D15 #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1412.4076
37 pages, 8 figures
openalex publication_date 2014/12/12 · arxiv created 2015/01/18 · arxiv updated 2015/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Within the field of phylogenetics there is great interest in distance measures to quantify the dissimilarity of two trees. Recently, a new distance measure has been proposed: the Maximum Parsimony (MP) distance. This is based on the difference of the parsimony scores of a single character on both trees under consideration, and the goal is to find the character which maximizes this difference. Here we show that computation of MP distance on two binary phylogenetic trees is NP-hard. This is a highly nontrivial extension of an earlier NP-hardness proof for two multifurcating phylogenetic trees, and it is particularly relevant given the prominence of binary trees in the phylogenetics literature. As a corollary to the main hardness result we show that computation of MP distance is also hard on binary trees if the number of states available is bounded. In fact, via a different reduction we show that it is hard even if only two states are available. Finally, as a first response to this hardness we give a simple Integer Linear Program (ILP) formulation which is capable of computing the MP distance exactly for small trees (and for larger trees when only a small number of character states are available) and which is used to computationally verify several auxiliary results required by the hardness proofs.