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URN: urn:nbn:de:0030-drops-49364
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### On Finding the Adams Consensus Tree

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### Abstract

This paper presents a fast algorithm for finding the Adams consensus tree of a set of conflicting phylogenetic trees with identical leaf labels, for the first time improving the time complexity of a widely used algorithm invented by Adams in 1972 [1]. Our algorithm applies the centroid path decomposition technique [9] in a new way to traverse the input trees' centroid paths in unison, and runs in O(k n \log n) time, where k is the number of input trees and n is the size of the leaf label set. (In comparison, the old algorithm from 1972 has a worst-case running time of O(k n^2).) For the special case of k = 2, an even faster algorithm running in O(n \cdot \frac{\log n}{\log\log n}) time is provided, which relies on an extension of the wavelet tree-based technique by Bose et al. [6] for orthogonal range counting on a grid. Our extended wavelet tree data structure also supports truncated range maximum queries efficiently and may be of independent interest to algorithm designers.

### BibTeX - Entry

@InProceedings{jansson_et_al:LIPIcs:2015:4936,
author =	{Jesper Jansson and Zhaoxian Li and Wing-Kin Sung},
title =	{{On Finding the Adams Consensus Tree}},
booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages =	{487--499},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-78-1},
ISSN =	{1868-8969},
year =	{2015},
volume =	{30},
editor =	{Ernst W. Mayr and Nicolas Ollinger},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},