An Algorithm for Consensus Trees
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We consider the tree consensus problem, an important problem in bioinformatics. Given a rooted tree t and another tree T, one would like to incorporate compatible information from T to t. This problem is a subproblem in the tree refinement problem called the RF-Optimal Tree Refinement Problem defined by in Christensen, Molloy, Vachaspati and Warnow [WABI'19] who employ the greedy algorithm by Gawrychowski, Landau, Sung, and Weimann [ICALP'18] that runs in time O(n^1.5log n). We give a faster algorithm for this problem that runs in time O(nlog n). Our key ingredient is a bipartition compatibility criteria based on amortized-time leaf counters. While this is an improvement, the fastest solution is an algorithm by Jansson, Shen, and Sung [JACM'16] which runs in time O(n).
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