Abstract
We combine two fundamental, previously studied optimization problems related to the construction of phylogenetic trees called maximum rooted triplets consistency (MAXRTC) and minimally resolved supertree (MINRS) into a new problem, which we call qmaximum rooted triplets consistency (qMAXRTC). The input to our new problem is a set R of resolved triplets (rooted, binary phylogenetic trees with three leaves each) and the objective is to find a phylogenetic tree with exactly q internal nodes that contains the largest possible number of triplets from R. We first prove that qMAXRTC is NPhard even to approximate within a constant ratio for every fixed q >= 2, and then develop various polynomialtime approximation algorithms for different values of q. Next, we show experimentally that representing a phylogenetic tree by one having much fewer nodes typically does not destroy too much triplet branching information. As an extreme example, we show that allowing only nine internal nodes is still sufficient to capture on average 80% of the rooted triplets from some recently published trees, each having between 760 and 3081 internal nodes. Finally, to demonstrate the algorithmic advantage of using trees with few internal nodes, we propose a new algorithm for computing the rooted triplet distance between two phylogenetic trees over a leaf label set of size n that runs in O(q n) time, where q is the number of internal nodes in the smaller tree, and is therefore faster than the currently best algorithms for the problem (with O(n log n) time complexity [SODA 2013, ESA 2017]) whenever q = o(log n).
BibTeX  Entry
@InProceedings{jansson_et_al:LIPIcs:2019:11031,
author = {Jesper Jansson and Konstantinos Mampentzidis and Sandhya T. P.},
title = {{Building a Small and Informative Phylogenetic Supertree}},
booktitle = {19th International Workshop on Algorithms in Bioinformatics (WABI 2019)},
pages = {1:11:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771238},
ISSN = {18688969},
year = {2019},
volume = {143},
editor = {Katharina T. Huber and Dan Gusfield},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/11031},
URN = {urn:nbn:de:0030drops110316},
doi = {10.4230/LIPIcs.WABI.2019.1},
annote = {Keywords: phylogenetic tree, supertree, rooted triplet, approximation algorithm}
}
Keywords: 

phylogenetic tree, supertree, rooted triplet, approximation algorithm 
Collection: 

19th International Workshop on Algorithms in Bioinformatics (WABI 2019) 
Issue Date: 

2019 
Date of publication: 

03.09.2019 