An Algorithm for Consensus Trees

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 $O(n^{1.5}\log n)$. We give a faster algorithm for this problem that runs in time $O(n\log n)$. 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 $O(n)$.