# New Reduction Rules for the Tree Bisection and Reconnection Distance

@article{Kelk2019NewRR, title={New Reduction Rules for the Tree Bisection and Reconnection Distance}, author={Steven M. Kelk and Simone Linz}, journal={Annals of Combinatorics}, year={2019}, pages={1-28} }

Recently it was shown that, if the subtree and chain reduction rules have been applied exhaustively to two unrooted phylogenetic trees, the reduced trees will have at most $$15k-9$$ 15 k - 9 taxa where k is the TBR (Tree Bisection and Reconnection) distance between the two trees, and that this bound is tight. Here, we propose five new reduction rules and show that these further reduce the bound to $$11k-9$$ 11 k - 9 . The new rules combine the “unrooted generator” approach introduced in Kelk…

## 3 Citations

Maximum parsimony distance on phylogenetictrees: a linear kernel and constant factor approximation algorithm

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 2021

This work proves that the maximum parsimony distance is fixed parameter tractable, that the problem permits a polynomial-time constant-factor approximation algorithm, and that the treewidth of a natural auxiliary graph structure encountered in phylogenetics is bounded by a function of the distance.

Parameterized Algorithms in Bioinformatics: An Overview

- Computer ScienceAlgorithms
- 2019

This work surveys recent developments of parameterized algorithms and complexity for important NP-hard problems in bioinformatics, and covers sequence assembly and analysis, genome comparison and completion, and haplotyping and phylogenetics.

Reflections on kernelizing and computing unrooted agreement forests

- Computer Science, BiologyAnn. 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.

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