 
Summary: Approximating Subtree Distances Between Phylogenies
Maria Luisa Bonet
Katherine St. John
Ruchi Mahindru§
Nina Amenta¶
August 14, 2006
Abstract
We give a 5approximation algorithm to the rooted SubtreePruneandRegraft
(rSPR) distance between two phylogenies, which was recently shown to be NPcomplete
by Bordewich and Semple [Bordewich and Semple, 2005]. This paper presents the first
approximation result for this important tree distance. The algorithm follows a standard
format for tree distances such as Rodrigues et al. [Rodrigues et al., 2001] and Hein et
al. [Hein et al., 1996]. The novel ideas are in the analysis. In the analysis, the cost of
the algorithm uses a "cascading" scheme that accounts for possible wrong moves. This
accounting is missing from previous analysis of tree distance approximation algorithms.
Lenguajes y Sistemas Informaticos (LSI), Universidad Politecnica de Catalunya (UPC), 08034 Barcelona,
Spain bonet@lsi.upc.edu.
Department of Math & Computer Science, Lehman College City University of New York (CUNY),
