On Finding the Adams Consensus Tree

Authors Jesper Jansson, Zhaoxian Li, Wing-Kin Sung

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Jesper Jansson
Zhaoxian Li
Wing-Kin Sung

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Jesper Jansson, Zhaoxian Li, and Wing-Kin Sung. On Finding the Adams Consensus Tree. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 487-499, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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.
  • phylogenetic tree
  • Adams consensus
  • centroid path
  • wavelet tree


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