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Reflections on kernelizing and computing unrooted agreement forests

Author

Listed:
  • Rim Wersch

    (Maastricht University)

  • Steven Kelk

    (Maastricht University)

  • Simone Linz

    (University of Auckland)

  • Georgios Stamoulis

    (Maastricht University)

Abstract

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 $$15k-9$$ 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.

Suggested Citation

  • Rim Wersch & Steven Kelk & Simone Linz & Georgios Stamoulis, 2022. "Reflections on kernelizing and computing unrooted agreement forests," Annals of Operations Research, Springer, vol. 309(1), pages 425-451, February.
    • Handle: RePEc:spr:annopr:v:309:y:2022:i:1:d:10.1007_s10479-021-04352-1
    DOI: 10.1007/s10479-021-04352-1
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    References listed on IDEAS

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    1. V. Chvatal, 1979. "A Greedy Heuristic for the Set-Covering Problem," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 233-235, August.
    2. Jochen Alber & Nadja Betzler & Rolf Niedermeier, 2006. "Experiments on data reduction for optimal domination in networks," Annals of Operations Research, Springer, vol. 146(1), pages 105-117, September.
    3. Ruriko Yoshida & Kenji Fukumizu & Chrysafis Vogiatzis, 2019. "Multilocus phylogenetic analysis with gene tree clustering," Annals of Operations Research, Springer, vol. 276(1), pages 293-313, May.
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