Bentert, Matthias ;
Malík, Josef ;
Weller, Mathias
Tree Containment With Soft Polytomies
Abstract
The Tree Containment problem has many important applications in the study of evolutionary history. Given a phylogenetic network N and a phylogenetic tree T whose leaves are labeled by a set of taxa, it asks if N and T are consistent. While the case of binary N and T has received considerable attention, the more practically relevant variant dealing with biological uncertainty has not. Such uncertainty manifests itself as highdegree vertices ("polytomies") that are "jokers" in the sense that they are compatible with any binary resolution of their children. Contrasting the binary case, we show that this problem, called Soft Tree Containment, is NPhard, even if N is a binary, multilabeled tree in which each taxon occurs at most thrice. On the other hand, we reduce the case that each label occurs at most twice to solving a 2SAT instance of size O(T^3). This implies NPhardness and polynomialtime solvability on reticulationvisible networks in which the maximum indegree is bounded by three and two, respectively.
BibTeX  Entry
@InProceedings{bentert_et_al:LIPIcs:2018:8835,
author = {Matthias Bentert and Josef Mal{\'i}k and Mathias Weller},
title = {{Tree Containment With Soft Polytomies}},
booktitle = {16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
pages = {9:19:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770682},
ISSN = {18688969},
year = {2018},
volume = {101},
editor = {David Eppstein},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8835},
URN = {urn:nbn:de:0030drops88353},
doi = {10.4230/LIPIcs.SWAT.2018.9},
annote = {Keywords: Phylogenetics, ReticulationVisible Networks, Multifurcating Trees}
}
2018
Keywords: 

Phylogenetics, ReticulationVisible Networks, Multifurcating Trees 
Seminar: 

16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)

Issue date: 

2018 
Date of publication: 

2018 