Phylogenetic analysis often produce a large number of candidate evolutionary trees, each a hypothesis of the "true" tree. Post-processing techniques such as strict consensus trees are widely used to summarize the evolutionary relationships into a single tree. However, valuable information is lost during the summarization process. A more elementary step is to produce estimates of the topological differences that exist among all pairs of trees. We design a new randomized algorithm, called Hash-RF, thatcomputes the all-to-all Robinson-Foulds (RF) distance--the most common distance metric for comparing two phylogenetic trees. Our approach uses a hash table to organize the bipartitions of a tree, and a universal hashing function makes our algorithm randomized. We compare the performance of our Hash-RF algorithm to PAUP*'s implementation of computing the all-to-all RF distance matrix. Our experiments focus on the algorithmic performance of comparing sets of biological trees, where the size of each treeranged from 500 to 2,000 taxa and the collection of trees varied from 200 to 1,000 trees. Our experimental results clearly show that our Hash-RF algorithm is up to 500 times faster than PAUP*'s approach. Thus, Hash-RF provides an efficient alternative to a single tree summary of a collection of trees and potentially gives researchers the ability to explore their data in new and interesting ways.
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