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

Jones, M.E.L.; Kelk, Steven; Stougie, Leen

doi:10.1016/j.jcss.2020.10.003

Maximum parsimony distance on phylogenetic trees

Title

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

Author

Jones, M.E.L. (TU Delft Discrete Mathematics and Optimization; Centrum Wiskunde & Informatica (CWI))
Kelk, Steven (Universiteit Maastricht)
Stougie, Leen (Centrum Wiskunde & Informatica (CWI); Vrije Universiteit Amsterdam; INRIA-Erable)

Date

2021

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.

Subject

Fixed parameter tractability
Maximum agreement forest
Maximum parsimony
Phylogenetics

To reference this document use:

http://resolver.tudelft.nl/uuid:8d5fc924-a45d-4472-a20c-54d511c45632

DOI

https://doi.org/10.1016/j.jcss.2020.10.003

ISSN

0022-0000

Source

Journal of Computer and System Sciences, 117, 165-181

Part of collection

Institutional Repository