eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-06-21
18:1
18:18
10.4230/LIPIcs.CPM.2023.18
article
On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem
Komusiewicz, Christian
1
https://orcid.org/0000-0003-0829-7032
Linz, Simone
2
https://orcid.org/0000-0003-0862-9594
Morawietz, Nils
3
https://orcid.org/0000-0002-7283-4982
Schestag, Jannik
3
https://orcid.org/0000-0001-7767-2970
Institute of Computer Science, Friedrich Schiller Universität Jena, Germany
School of Computer Science, University of Auckland, New Zealand
Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Germany
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol259-cpm2023/LIPIcs.CPM.2023.18/LIPIcs.CPM.2023.18.pdf
phylogenetic trees
parameterized complexity
tree distances
NNI
TBR