Reflections on kernelizing and computing unrooted agreement forests

Author:

van Wersch Rim,Kelk Steven,Linz Simone,Stamoulis GeorgiosORCID

Abstract

AbstractPhylogenetic trees are leaf-labelled trees used to model the evolution of species. Here we explore 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. This problem is better-known in the literature as the maximum agreement forest problem, where the goal is to partition the two trees into a minimum number of common, non-overlapping subtrees. We have implemented two well-known reduction rules, the subtree and chain reduction, and five more recent, theoretically stronger reduction rules, and compare the reduction achieved with and without the stronger rules. We find that the new rules yield smaller reduced instances and thus have clear practical added value. In many cases they also cause the TBR distance to decrease in a controlled fashion, which can further facilitate solving the problem in practice. Next, we compare the achieved reduction to the known worst-case theoretical bounds of $$15k-9$$ 15 k - 9 and $$11k-9$$ 11 k - 9 respectively, on the number of leaves of the two reduced trees, where k is the TBR distance, observing in both cases a far larger reduction in practice. As a by-product of our experimental framework we obtain a number of new insights into the actual computation of TBR distance. We find, for example, that very strong lower bounds on TBR distance can be obtained efficiently by randomly sampling certain carefully constructed partitions of the leaf labels, and identify instances which seem particularly challenging to solve exactly. The reduction rules have been implemented within our new solver Tubro which combines kernelization with an Integer Linear Programming (ILP) approach. Tubro also incorporates a number of additional features, such as a cluster reduction and a practical upper-bounding heuristic, and it can leverage combinatorial insights emerging from the proofs of correctness of the reduction rules to simplify the ILP.

Publisher

Springer Science and Business Media LLC

Subject

Management Science and Operations Research,General Decision Sciences

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Deep kernelization for the Tree Bisection and Reconnection (TBR) distance in phylogenetics;Journal of Computer and System Sciences;2024-06

2. A near-linear kernel for bounded-state parsimony distance;Journal of Computer and System Sciences;2024-03

3. Convex Characters, Algorithms, and Matchings;SIAM Journal on Discrete Mathematics;2024-01-19

4. Relaxed Agreement Forests;Lecture Notes in Computer Science;2024

5. Sharp Upper and Lower Bounds on a Restricted Class of Convex Characters;The Electronic Journal of Combinatorics;2022-03-11

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