The Balanced Minimum Evolution Problem

References

• Applegate D., Bixby R., Chvátal V., Cook W. (2001) . Retrieved April 7, 2011, Concorde, TSP solver. http://www.tsp.gatech.edu/concorde.htmlGoogle Scholar
• Bader D. A., Moret B. M. E., Vawter L. Industrial applications of high-performance computing for phylogeny reconstruction. SPIE ITCom 2001 (2001) (SPIE, Denver) 159–168Google Scholar
• Beyer W. A., Stein M., Smith T., Ulam S. A molecular sequence metric and evolutionary trees. Math. Biosci. (1974) 19(1–2):9–25Crossref, Google Scholar
• Buneman P. A note on the metric properties of trees. J. Combin. Theory Ser. B (1974) 17:48–50Crossref, Google Scholar
• Bush R. M., Bender C. A., Subbarao K., Cox N. J., Fitch W. M. Predicting the evolution of human influenza A. Science (1999) 286(5446):1921–1925Crossref, Google Scholar
• Catanzaro D. The minimum evolution problem: Overview and classification. Networks (2009) 53(2):112–125Crossref, Google Scholar
• Catanzaro D., Bruni R. Estimating phylogenies from molecular data. Mathematical Approaches to Polymer Sequence Analysis and Related Problems (2011) (Springer, New York) 149–176Crossref, Google Scholar
• Catanzaro D., Pesenti R., Milinkovitch M. A non-linear optimization procedure to estimate distances and instantaneous substitution rate matrices under the GTR model. Bioinformatics (2006) 22(6):708–715Crossref, Google Scholar
• Catanzaro D., Labbé M., Pesenti R., Salazar-Gonzáles J. J. The balanced minimum evolution problem. (2008) . Techical report, Computer Science Department, Université Libre de Bruxelles, BruxellesGoogle Scholar
• Catanzaro D., Labbé M., Pesenti R., Salazar-Gonzáles J. J. Mathematical models to reconstruct phylogenetic trees under the minimum evolution criterion. Networks (2009) 53(2):126–140Crossref, Google Scholar
• Chang B. S., Donoghue M. J. Recreating ancestral proteins. Trends Ecology Evol. (2000) 15(3):109–114Crossref, Google Scholar
• Desper R., Gascuel O. Fast and accurate phylogeny reconstruction algorithms based on the minimum-evolution principle. J. Comput. Biol. (2002) 9(5):687–705Crossref, Google Scholar
• Desper R., Gascuel O. Theoretical foundation of the balanced minimum evolution method of phylogenetic inference and its relationship to the weighted least-squares tree fitting. Molecular Biol. Evol. (2004) 21:587–598Crossref, Google Scholar
• Desper R., Gascuel O., Gascuel O. The minimum evolution distance-based approach to phylogenetic inference. Mathematics of Evolution and Phylogeny (2005) (Oxford University Press, New York) 1–32Chapter 1Crossref, Google Scholar
• Felsenstein J.Inferring Phylogenies (2004) (Sinauer Associates, Sunderland, MA) Google Scholar
• Fiorini S., Joret G. The balanced minimum evolution problem is hard. (2010) . Technical report, Département de Mathématique, Université Libre de Bruxelles, BruxellesGoogle Scholar
• Fischetti M., Lancia G., Serafini P. Exact algorithms for minimum routing cost trees. Networks (2002) 39(3):161–173Crossref, Google Scholar
• Garey M. R., Johnson D. S.Computers and Intractability: A Guide to the Theory of NP-Completeness (2003) (Freeman, New York) Google Scholar
• Harvey P. H., Brown A. J. L., Smith J. M., Nee S.New Uses for New Phylogenies (1996) (Oxford University Press, Oxford, UK) Crossref, Google Scholar
• Marra M. A., Jones S. J., Astell C. R., Holt R. A., Brooks-Wilson A., Butterfield Y. S., Khattra J., et al. The genome sequence of the SARS-associated coronavirus. Science (2003) 300(5624):1399–1404Crossref, Google Scholar
• Maurras J. F., Nguyen T. H., Nguyen V. H. On the convex hull of Huffman trees. Electron. Notes Discrete Math. (2010) 36:1009–1016Crossref, Google Scholar
• Ou C. Y., Ciesielski C. A., Myers G., Bandea C. I., Luo C. C., Korber B. T. M., Mullins J. I., et al. Molecular epidemiology of HIV transmission in a dental practice. Science (1992) 256(5060):1165–1171Crossref, Google Scholar
• Pachter L., Sturmfels B. The mathematics of phylogenomics. SIAM Rev. (2007) 49:3–31Crossref, Google Scholar
• Pardi F. Algorithms on phylogenetic trees. (2009) . Ph.D. thesis, University of Cambridge, Cambridge, UKGoogle Scholar
• Parker D. S., Ram P. The construction of Huffman codes is a submodular (“convex”) optimization problem over a lattice of binary trees. SIAM J. Comput. (1996) 28(5):1875–1905Crossref, Google Scholar
• Pauplin Y. Direct calculation of a tree length using a distance matrix. J. Molecular Evol. (2000) 51(1):41–47Crossref, Google Scholar
• Ross H. A., Rodrigo A. G. Immune-mediated positive selection drives human immunodeficency virus type 1 molecular variation and predicts disease duration. J. Virology (2002) 76(22):11715–11720Crossref, Google Scholar
• Semple C., Steel M. Cyclic permutations and evolutionary trees. Adv. Appl. Math. (2004) 32(4):669–680Crossref, Google Scholar
• Waterman M. S., Smith T. F., Singh M., Beyer W. A. Additive evolutionary trees. J. Theoret. Biol. (1977) 64(2):199–213Crossref, Google Scholar