New Reduction Rules for the Tree Bisection and Reconnection Distance

  title={New Reduction Rules for the Tree Bisection and Reconnection Distance},
  author={Steven M. Kelk and Simone Linz},
  journal={Annals of Combinatorics},
  • S. Kelk, S. Linz
  • Published 4 May 2019
  • Computer Science, Mathematics, Biology
  • Annals of Combinatorics
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… Expand
3 Citations
Maximum parsimony distance on phylogenetictrees: a linear kernel and constant factor approximation algorithm
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. Expand
Parameterized Algorithms in Bioinformatics: An Overview
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. Expand
Reflections on kernelizing and computing unrooted agreement forests
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. Expand


A tight kernel for computing the tree bisection and reconnection distance between two phylogenetic trees
  • S. Kelk, S. Linz
  • Mathematics, Computer Science
  • SIAM J. Discret. Math.
  • 2019
This work reanalyse Allen and Steel's kernelization algorithm and proves that the reduced instances will in fact have at most 15k-9 taxa, and introduces and uses "unrooted generators" which are analogues of rooted structures that have appeared earlier in the phylogenetic networks literature. Expand
Extremal Distances for Subtree Transfer Operations in Binary Trees
It is shown that for a pair of leaf-labelled binary trees with n leaves, the maximum number of such moves required to transform one into the other is n-Theta (n-Θ(n), extending a result of Ding, Grünewald, and Humphries. Expand
On the fixed parameter tractability of agreement-based phylogenetic distances
New analyses are presented showing that the use of the “cluster reduction” rule—already defined for the hybridization number and the rSPR distance and introduced here for the TBR distance—can transform any algorithm for solving three important measures of dissimilarity in phylogenetic trees into an O(f(k)·n)-time one. Expand
Subtree Transfer Operations and Their Induced Metrics on Evolutionary Trees
Abstract. Leaf-labelled trees are widely used to describe evolutionary relationships, particularly in biology. In this setting, extant species label the leaves of the tree, while the internalExpand
On Unrooted and Root-Uncertain Variants of Several Well-Known Phylogenetic Network Problems
The fundamental problem of determining whether an unrooted phylogenetic network displays (i.e. embeds) a phylogenetic tree, is NP-hard and it is shown that the problem is FPT in the hybridization number, via kernelization, for any number of input trees. Expand
On the Complexity of Comparing Evolutionary Trees
For the maximum refinement subtree (MRST) problem involving two trees, it is shown that it is polynomialtime solvable when both trees have bounded degree and is NP-hard when one of the trees can have an arbitrary degree. Expand
On the Maximum Parsimony Distance Between Phylogenetic Trees
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. Expand
Parameterized Algorithms for the Maximum Agreement Forest Problem on Multiple Rooted Multifurcating Trees
A generalized version of the problem: the Maximum Agreement Forest problem on multiple rooted multifurcating phylogenetic trees, from the perspective of fixed-parameter algorithms is studied, taking advantage of a new branch-and-bound strategy. Expand
Hybrids in real time.
A simple result is presented to show that, despite the presence of Reticulation, there is always a well-defined underlying tree that corresponds to those parts of life that do not have a history of reticulation. Expand
Parameterized and approximation algorithms for maximum agreement forest in multifurcating trees
This work studies parameterized algorithms and approximation algorithms for the maximum agreement forest problem, which, for two given leaf-labeled trees, is to find a maximum forest that is a subgraph of both trees, giving the first constant-ratio approximation algorithm for general trees. Expand