Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Case Study: Visualizing Sets of Evolutionary Trees
INFOVIS '02 Proceedings of the IEEE Symposium on Information Visualization (InfoVis'02)
Database-friendly random projections: Johnson-Lindenstrauss with binary coins
Journal of Computer and System Sciences - Special issu on PODS 2001
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
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The Robinson-Foulds (RF) metric is the measure most widely used in comparing phylogenetic trees; it can be computed in linear time using Day's algorithm. When faced with the need to compare large numbers of large trees, however, even linear time becomes prohibitive. We present a randomized approximation scheme that provides, with high probability, a (1+ε) approximation of the true RF metric for all pairs of trees in a given collection. Our approach is to use a sublinear-space embedding of the trees, combined with an application of the Johnson-Lindenstrauss lemma to approximate vector norms very rapidly. We discuss the consequences of various parameter choices (in the embedding and in the approximation requirements). We also implemented our algorithm as a Java class that can easily be combined with popular packages such as Mesquite; in consequence, we present experimental results illustrating the precision and running-time tradeoffs as well as demonstrating the speed of our approach.