CSDL Home IEEE/ACM Transactions on Computational Biology and Bioinformatics 2013 vol.10 Issue No.01 - Jan.-Feb.

Subscribe

Issue No.01 - Jan.-Feb. (2013 vol.10)

pp: 236-239

Alan Joseph J. Caceres , Dept. of Math. & Comput. Sci., City Univ. of New York, New York, NY, USA

Juan Castillo , Dept. of Math. & Comput. Sci., City Univ. of New York, New York, NY, USA

Jinnie Lee , Dept. of Math. & Comput. Sci., City Univ. of New York, New York, NY, USA

Katherine St. John , Dept. of Math. & Comput. Sci., City Univ. of New York, New York, NY, USA

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TCBB.2012.136

ABSTRACT

A nearest-neighbor-interchange (NNI)-walk is a sequence of unrooted phylogenetic trees, T

_{1},T_{2}, ... ,T_{k}where each consecutive pair of trees differs by a single NNI move. We give tight bounds on the length of the shortest NNI-walks that visit all trees in a subtree-prune-and-regraft (SPR) neighborhood of a given tree. For any unrooted, binary tree, T, on n leaves, the shortest walk takes ⊖(n^{2}) additional steps more than the number of trees in the SPR neighborhood. This answers Bryant's Second Combinatorial Challenge from the Phylogenetics Challenges List, the Isaac Newton Institute, 2011, and the Penny Ante Problem List, 2009.INDEX TERMS

Nearest neighbor searches, Decision trees,graphs and networks, Analysis of algorithms and problem complexity, biology and genetics, trees

CITATION

Alan Joseph J. Caceres, Juan Castillo, Jinnie Lee, Katherine St. John, "Walks on SPR Neighborhoods",

*IEEE/ACM Transactions on Computational Biology and Bioinformatics*, vol.10, no. 1, pp. 236-239, Jan.-Feb. 2013, doi:10.1109/TCBB.2012.136REFERENCES

- [1] B. Allen and M. Steel, “Subtree Transfer Operations and their Induced Metrics on Evolutionary Trees,”
Ann. Combinatorics, vol. 5, pp. 1-13, 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 Suaft Distance,”
Ann. Combinatorics, vol. 8, pp. 409-423, 2004.- [5] D. Bryant, “Annual New Zealand Phylogenetics Meeting (Kaikoura 2009) Penny Ante prize problems: A Mathematical Challenge,” http://www.math.canterbury.ac.nz/bio/events/ kaikoura09penny.shtml, 2009.
- [6] D. Bryant, personal communication, 2012.
- [7] A.J.J Caceres, S. Daley, J. DeJesus, M. Hintze, D. Moore, and K. St. John, “Walks in Phylogenetic Treespace,”
Information Processing Letters, vol. 111, pp. 600-604, 2011.- [8] B. DasGupta, X. He, T. Jiang, M. Li, J. Tromp, and L. Zhang, “On Computing the Nearest Neighbor Interchange Distance,”
Proc. Workshop Discrete Problems with Medical Applications vol. 55, pp. 125-143, 2000.- [9] L.R. Foulds and R.L. Graham, “The Steiner Problem in Phylogeny is NP-Complete,”
Advances in Applied Math., vol. 3, no. 1, pp. 43-49, 1982.- [10] P.A. Goloboff, J.S. Farris, and K.C. Nixon, “TNT, a Free Program for Phylogenetic Analysis,”
Cladistics, vol. 24, pp. 774-786, 2008.- [11] G. Hickey, F. Dehne, A. Rau-Chaplin, and C. Blouin, “SPR Distance Computation for Unrooted Trees,”
Evolutionary Bioinformatics, vol. 4, pp. 17-27, 2008.- [12] D.M. Hillis, B.K. Mable, and C. Moritz,
Molecular Systematics. Sinauer Assoc., 1996.- [13] J.P. Huelsenbeck and F. Ronquist, “MrBayes: Bayesian Inference of Phylogeny,”
Bioinformatics, vol. 17, no. 8, pp. 754-755, 2001.- [14] M. Li, J. Tromp, and L. Zhang, “Some Notes on the Nearest Neighbour Interchange Distance,”
Proc. Second Ann. Int'l Conf. Computing and Combinatorics (COCOON '96), pp. 343-351, 1996.- [15] S. Roch, “A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood is Hard,”
IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 3, no. 1, pp. 92-94, Jan. 2006.- [16] C. Semple and M. Steel,
Phylogenetics, Oxford Lecture Series in Mathematics and Its Applications, vol. 24, Oxford Univ. Press, 2003.- [17] M. Steel, “Challenges and Conjectures: ISAAC Newton Institute Phylogenetics Program 2011,” http://www.newton.ac.uk/programmes/PLGphylogenetics_challenges.pdf , 2012.
- [18] D.L. Swofford,
PAUP*. Phylogenetic Analysis Using Parsimony (*and Other Methods), Version 4. Sinauer Assoc., 2002.- [19] S. Whelan, “New Approaches to Phylogenetic Tree Search and Their Application to Large Numbers of Protein Alignments.”
Systematic Biology, vol. 56, no. 5, pp. 727-740, 2007. |