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Maximizing Phylogenetic Diversity Under Ecological Constraints: A Parameterized Complexity Study

Authors Christian Komusiewicz , Jannik Schestag

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Christian Komusiewicz
  • Institute of Computer Science, Friedrich Schiller University Jena, Germany
Jannik Schestag
  • Institute of Computer Science, Friedrich Schiller University Jena, Germany

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Christian Komusiewicz and Jannik Schestag. Maximizing Phylogenetic Diversity Under Ecological Constraints: A Parameterized Complexity Study. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FSTTCS.2024.28

Abstract

In the NP-hard Optimizing Phylogenetic Diversity with Dependencies(PDD) problem, the input consists of a phylogenetic tree 𝒯 over a set of taxa X, a food-web that describes the prey-predator relationships in X, and integers k and D. The task is to find a set S of k species that is viable in the food-web such that the subtree of 𝒯 obtained by retaining only the vertices of S has total edge weight at least D. Herein, viable means that for every predator taxon of S, the set S contains at least one prey taxon.
We provide the first systematic analysis of PDD and its special case with star trees, s-PDD, from a parameterized complexity perspective. For solution-size related parameters, we show that PDD is fixed-parameter tractable (FPT) with respect to D and with respect to k plus the height of the phylogenetic tree. Moreover, we consider structural parameterizations of the food-web. For example, we show an FPT-algorithm for the parameter that measures the vertex deletion distance to graphs where every connected component is a complete graph. Finally, we show that s-PDD admits an FPT-algorithm for the treewidth of the food-web. This disproves, unless P = NP, a conjecture of Faller et al. [Annals of Combinatorics, 2011] who conjectured that s-PDD is NP-hard even when the food-web is a tree.

Subject Classification

ACM Subject Classification
  • Applied computing → Computational biology
  • Theory of computation → Fixed parameter tractability
Keywords
  • phylogenetic diversity
  • food-webs
  • structural parameterization
  • color-coding
  • dynamic programming

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