# On the Complexity of Computing MP Distance Between Binary Phylogenetic Trees

@article{Kelk2014OnTC, title={On the Complexity of Computing MP Distance Between Binary Phylogenetic Trees}, author={Steven M. Kelk and Mareike Fischer}, journal={Annals of Combinatorics}, year={2014}, volume={21}, pages={573-604} }

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…

## 16 Citations

Reduction rules for the maximum parsimony distance on phylogenetic trees

- Computer ScienceTheor. Comput. Sci.
- 2016

Phylogenetic incongruence through the lens of Monadic Second Order logic

- MathematicsJ. Graph Algorithms Appl.
- 2016

This article uses Monadic Second Order logic (MSOL) to give alternative, compact proofs of fixed parameter tractability for several well-known incongruency measures and introduces a number of "phylogenetics MSOL primitives" which will hopefully be of use to other researchers.

A note on convex characters and Fibonacci numbers

- MathematicsArXiv
- 2015

This work proves that the number of convex characters in which each state appears on at least two taxa, is independent of topology, and equal to the (n-1)th Fibonacci number, and gives a simple but effective algorithm for the NP-hard "maximum parsimony distance" problem.

A note on convex characters, Fibonacci numbers and exponential-time algorithms

- Computer ScienceAdv. Appl. Math.
- 2017

Convex characters, algorithms and matchings

- Computer Science
- 2021

This work shows how combining the enumeration of convex characters with existing parameterised algorithms can be used to speed up exponential-time algorithms for the maximum agreement forest problem in phylogenetics, and re-visits the quantity g2(T), defined as the number of conveX characters on T in which each state appears on at least 2 taxa.

Neighborhoods of Phylogenetic Trees: Exact and Asymptotic Counts

- MathematicsSIAM J. Discret. Math.
- 2016

A number of exact and asymptotic results concerning the size and structure of the neighbourhoods of trees under tree rearrangement operations are provided, and some key aspects of tree shape that play a role in determining these quantities are identified.

Reflections on kernelizing and computing unrooted agreement forests

- Computer ScienceAnn. Oper. Res.
- 2022

This work explores the practical impact of kernelization (i.e. data reduction) on the NP-hard problem of computing the TBR distance between two unrooted binary phylogenetic trees and finds that the new rules yield smaller reduced instances and thus have clear practical added value.

Gromov meets Phylogenetics - new Animals for the Zoo of Biocomputable Metrics on Tree Space

- Computer Science, Mathematics
- 2015

We present a new class of metrics for unrooted phylogenetic $X$-trees derived from the Gromov-Hausdorff distance for (compact) metric spaces. These metrics can be efficiently computed by linear or…

A Linear Bound on the Number of States in Optimal Convex Characters for Maximum Parsimony Distance

- Computer ScienceIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2017

This note proves that for binary trees there exists a character achieving this maximum that is convex on one of the trees (i.e., the parsimony score induced on that tree is equal to the number of states in the character minus 1) and such that the number-of-state bound is at most 7d_\mathrm{MP}-5.

## References

SHOWING 1-10 OF 17 REFERENCES

On the Maximum Parsimony Distance Between Phylogenetic Trees

- Computer Science
- 2014

This article shows that this new distance is a metric and provides a lower bound to the well-known Subtree Prune and Regraft (SPR) distance, and shows that to compute the MP distance it is sufficient to consider only characters that are convex on one of the trees, and proves several additional structural properties of the distance.

Revisiting an Equivalence Between Maximum Parsimony and Maximum Likelihood Methods in Phylogenetics

- BiologyBulletin of mathematical biology
- 2010

It is shown that in these cases, even under no common mechanism, maximum parsimony and maximum likelihood might make conflicting choices, and if there is an upper bound on the substitution probabilities which is ‘sufficiently small’, every maximum likelihood tree is also a maximum Parsimony tree (but not vice versa).

RECONSTRUCTING CHARACTER EVOLUTION ON POLYTOMOUS CLADOGRAMS

- Biology
- 1989

New algorithms for both ordered and unordered characters are presented to reconstruct character evolution under the uncertain‐resolution interpretation of polytomies, which allow the cladogram to resolve itself so as to be favourable for the character whose evolution is being reconstructed.

MINIMUM MUTATION FITS TO A GIVEN TREE

- Biology
- 1973

A method of generating all such minimum mutation fits is described, which is the assignment which permits representation of the data in a minimum number of symbols, which seems compelling in its own right.

On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance

- Computer Science
- 2005

This paper shows that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard, and shows that this distance is fixed parameter tractable when parameterised by the distance between the two trees.

A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees

- Computer Science, BiologyBMC Bioinformatics
- 2013

Using simulations, CycleKiller and NonbinaryCycleKiller are presented, the first methods to produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations.

Optimization, Approximation, and Complexity Classes

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 1991

A natural variant of NP, MAX NP, and also a subclass called MAX SNP are defined, which contain several natural, well-studied classes of optimization problems, and it is shown that problems in these classes can be approximated with some bounded error.

Graph Theory

- Mathematics
- 1997

Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results.

Some APX-completeness results for cubic graphs

- MathematicsTheor. Comput. Sci.
- 2000

The NP-Completeness of Edge-Coloring

- MathematicsSIAM J. Comput.
- 1981

It is shown that it is NP-complete to determine the chromatic index of an arbitrary graph, even for cubic graphs.