Maximum parsimony distance on phylogenetic trees: A linear kernel and constant factor approximation algorithm

Mark Jones, Steven Kelk, Leen Stougie

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Abstract

Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we address this shortcoming by showing that the problem is fixed parameter tractable. We do this by establishing a linear kernel i.e., that after applying certain reduction rules the resulting instance has size that is bounded by a linear function of the distance. As powerful corollaries to this result we prove that the problem permits a polynomial-time constant-factor approximation algorithm; that the treewidth of a natural auxiliary graph structure encountered in phylogenetics is bounded by a function of the distance; and that the distance is within a constant factor of the size of a maximum agreement forest of the two trees, a well studied object in phylogenetics.

Original languageEnglish
Pages (from-to)165-181
Number of pages17
JournalJournal of Computer and System Sciences
Volume117
DOIs
Publication statusPublished - 2021

Keywords

  • Fixed parameter tractability
  • Maximum agreement forest
  • Maximum parsimony
  • Phylogenetics

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