Reflections on kernelizing and computing unrooted agreement forests

@article{Wersch2022ReflectionsOK,
  title={Reflections on kernelizing and computing unrooted agreement forests},
  author={Rim van Wersch and Steven M. Kelk and Simone Linz and Georgios Stamoulis},
  journal={Annals of Operations Research},
  year={2022},
  volume={309},
  pages={425-451}
}
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… 
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Methods Citations
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3 Citations

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Citation Type

Deep kernelization for the Tree Bisection and Reconnnect (TBR) distance in phylogenetics
TLDR
A kernel of size 9k − 8 is described for the NP-hard problem of computing the Tree Bisection and Reconnect distance k between two unrooted binary phylogenetic trees by extending the existing portfolio of reduction rules with three novel new reduction rules.
Convex characters, algorithms and matchings
TLDR
This work shows how combining the enumeration of convex characters with existing parameterised algorithms can be used to speed up exponential-time algorithms for the maximum agreement forest problem in phylogenetics, and re-visits the quantity g2(T), defined as the number of conveX characters on T in which each state appears on at least 2 taxa.
Sharp Upper and Lower Bounds on a Restricted Class of Convex Characters
TLDR
For every k ≥ 3 topological neutrality no longer holds, tree topologies achieving the maximum and minimum values of gk are described and corresponding expressions and exponential bounds are determined.

References

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