Abstract
Synthesizing large-scale phylogenetic trees is a fundamental problem in evolutionary biology. Median tree problems have evolved as a powerful tool to reconstruct such trees. Given a tree collection, these problems seek a median tree under some problem-specific tree distance. Here, we introduce the median tree problem for the classical path-difference distance. We prove that this problem is NP-hard, and describe a fast local search heuristic that is based on solving a local search problem exactly. For an effective heuristic we devise a time efficient algorithm for this problem that improves on the best-know (naive) solution by a factor of n, where n is the size of the input trees. Finally, we demonstrate the performance of our heuristic in a comparative study with other commonly used methods that synthesize species trees using published empirical data sets.
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