On the Complexity of Computing MP Distance Between Binary Phylogenetic Trees
- 106 Downloads
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.
Mathematics Subject Classification05C15 05C35 90C35 92D15
KeywordsMaximum Parsimony phylogenetics tree metrics NP-hard binary trees
- 4.Archie, J., Day, W., Felsenstein, J., Maddison, W., Meacham, C., Rohlf, F., Swofford, D.: The newick tree format. (2000) http://evolution.genetics.washington.edu/phylip/newicktree.html
- 9.Haws, D., Hodge, T., Yoshida, R.: Phylogenetic tree reconstruction: geometric approaches. In: Robeva, R., Hodge, T. (eds.)Mathematical Concepts andMethods inModern Biology: Using Modern Discrete Models, pp. 307–342. Elsevier, Dublin (2013)Google Scholar
- 13.Kelk, S., Fischer, M.: Maximum parsimony distance integer linear program (MPDIST). ”http://skelk.sdf-eu.org/mpdistbinary/” (2014)
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.