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DOI: 10.4230/LIPIcs.CPM.2023.18

On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem

Authors: Christian Komusiewicz, Simone Linz, Nils Morawietz, and Jannik Schestag

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)

Abstract

Maximum Parsimony is the problem of computing a most parsimonious phylogenetic tree for a taxa set X from character data for X. A common strategy to attack this notoriously hard problem is to perform a local search over the phylogenetic tree space. Here, one is given a phylogenetic tree T and wants to find a more parsimonious tree in the neighborhood of T. We study the complexity of this problem when the neighborhood contains all trees within distance k for several classic distance functions. For the nearest neighbor interchange (NNI), subtree prune and regraft (SPR), tree bisection and reconnection (TBR), and edge contraction and refinement (ECR) distances, we show that, under the exponential time hypothesis, there are no algorithms with running time |I|^o(k) where |I| is the total input size. Hence, brute-force algorithms with running time |X|^𝒪(k) ⋅ |I| are essentially optimal. In contrast to the above distances, we observe that for the sECR-distance, where the contracted edges are constrained to form a subtree, a better solution within distance k can be found in k^𝒪(k) ⋅ |I|^𝒪(1) time.

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Christian Komusiewicz, Simone Linz, Nils Morawietz, and Jannik Schestag. On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{komusiewicz_et_al:LIPIcs.CPM.2023.18,
  author =	{Komusiewicz, Christian and Linz, Simone and Morawietz, Nils and Schestag, Jannik},
  title =	{{On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.18},
  URN =		{urn:nbn:de:0030-drops-179729},
  doi =		{10.4230/LIPIcs.CPM.2023.18},
  annote =	{Keywords: phylogenetic trees, parameterized complexity, tree distances, NNI, TBR}
}

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DOI: 10.4230/DagRep.9.10.134

Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443)

Authors: Magnus Bordewich, Britta Dorn, Simone Linz, and Rolf Niedermeier

Published in: Dagstuhl Reports, Volume 9, Issue 10 (2020)

Abstract

Phylogenetics is the study of ancestral relationships between species. Its central goal is the reconstruction and analysis of phylogenetic trees and networks. Even though research in phylogenetics is motivated by biological questions and applications, it heavily relies on mathematics and computer science. Dagstuhl Seminar 19443 on Algorithms and Complexity in Phylogenetics aimed at bringing together researchers from phylogenetics and theoretical computer science to enable an exchange of expertise, facilitate interactions across both research areas, and establish new collaborations. This report documents the program and outcomes of the seminar. It contains an executive summary, abstracts of talks, short summaries of working groups, and a list of open problems that were posed during the seminar.

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Magnus Bordewich, Britta Dorn, Simone Linz, and Rolf Niedermeier. Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443). In Dagstuhl Reports, Volume 9, Issue 10, pp. 134-151, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Article{bordewich_et_al:DagRep.9.10.134,
  author =	{Bordewich, Magnus and Dorn, Britta and Linz, Simone and Niedermeier, Rolf},
  title =	{{Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443)}},
  pages =	{134--151},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2020},
  volume =	{9},
  number =	{10},
  editor =	{Bordewich, Magnus and Dorn, Britta and Linz, Simone and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.10.134},
  URN =		{urn:nbn:de:0030-drops-118590},
  doi =		{10.4230/DagRep.9.10.134},
  annote =	{Keywords: Approximation algorithms, Evolution, Parameterized algorithms, Phylogenetic trees and networks}
}

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Documents authored by Linz, Simone

On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem

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Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443)

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