Reflections on kernelizing and computing unrooted agreement forests

R. van Wersch, S. Kelk, S. Linz, G. Stamoulis*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


Phylogenetic 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 and 11k- 9 respectively, on the number of leaves of the two reduced trees, where k is the TBRdistance, 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.
Original languageEnglish
Pages (from-to)425-451
Number of pages27
JournalAnnals of Operations Research
Issue number1
Early online date19 Nov 2021
Publication statusPublished - Feb 2022


  • Phylogenetics
  • Agreement forest
  • TBR distance
  • Kernelization
  • Fixed parameter tractability


Dive into the research topics of 'Reflections on kernelizing and computing unrooted agreement forests'. Together they form a unique fingerprint.

Cite this