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On the Complexity of uSPR Distance
July-September 2010 (vol. 7 no. 3)
pp. 572-576
Maria Luisa Bonet, Universitat Politècnica de Catalunya (UPC), Barcelona
Katherine St. John, City University of New York (CUNY), Bronx
We show that subtree prune and regraft (uSPR) distance on unrooted trees is fixed parameter tractable with respect to the distance. We also make progress on a conjecture of Steel [9] on the preservation of uSPR distance under chain reduction, improving on lower bounds of Hickey et al. [7].

[1] B.L. Allen and M. Steel, "Subtree Transfer Operations and Their Induced Metrics on Evolutionary Trees," Annals of Combinatorics, vol. 5, no. 1, pp. 1-15, 2001.
[2] M.L. Bonet, K.St. John, R. Mahindru, and N. Amenta, "Approximating Subtree Distances between Phylogenies," J. Computational Biology, vol. 13, no. 8, pp. 1419-1434, 2006.
[3] M. Bordewich, C. McCartin, and C. Semple, "A 3-Approximation Algorithm for the Subtree Distance between Phylogenies," J. Discrete Algorithms, vol. 6, no. 3, pp. 458-471, 2008.
[4] M. Bordewich and C. Semple, "On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance," Annals of Combintorics, vol. 8, pp. 409-423, 2004.
[5] M. Hallett and C. McCartin, "A Faster FPT Algorithm for the Maximum Agreement Forest Problem," Theory of Computing Systems, vol. 41, no. 3, pp. 539-550, 2007.
[6] J. Hein, T. Jiang, L. Wang, and K. Zhang, "On the Complexity of Comparing Evolutionary Trees," Discrete Applied Math., vol. 71, nos. 1-3, pp. 153-169, 1996.
[7] G. Hickey, F. Dehne, A. Rau-Chaplin, and C. Blouin, "SPR Distance Computation for Unrooted Trees," Evolutionary Bioinformatics, vol. 4, pp. 17-27, 2008.
[8] C. McCartin, personal comm., 2008.
[9] M. Steel, "SPR Conjecture," www.math.canterbury.ac.nz/~m.steel/ research reward2.pdf, 2002.
[10] D.L. Swofford, G.J. Olsen, P.J. Waddell, and D.M. Hillis, "Phylogenetic Inference," Molecular Systematics, second ed., pp. 407-514, Sinauer, 1996.

Index Terms:
Phylogeny, analysis of algorithms, fixed parameter tractability.
Citation:
Maria Luisa Bonet, Katherine St. John, "On the Complexity of uSPR Distance," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 7, no. 3, pp. 572-576, July-Sept. 2010, doi:10.1109/TCBB.2008.132
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