Efficient Local Search for Euclidean Path-Difference Median Trees

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. Such problems seek a median tree for a given collection of input trees under some problem-specific tree distance. There has been an increased interest in the median tree problem for the classical path-difference distance between trees. While this problem is NP-hard, standard local search heuristics have been described that are based on solving a local search problem exactly. For a more effective heuristic we devise a time efficient algorithm for the local search problem that improves on the best-known solution by a factor of $n$n, where $n$n is the size of the input trees. Furthermore, we introduce a novel hybrid version of the standard local search that is exploiting our new algorithm for a more refined heuristic search. Finally, we demonstrate the performance of our hybrid heuristic in a comparative study with other commonly used methods that synthesize species trees using published empirical data sets.