A few logs suffice to build (almost) all trees (I)

Random Structures and Algorithms

Volumn 14, Issue 2, 1999, Pages 153-184

  Erdos, Péter L ^a   Steel, Michael A ^b   Székely, Lászlo A ^c   Warnow, Tandy J ^d  

^a ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

^b UNIVERSITY OF CANTERBURY   (New Zealand)

^c UNIVERSITY OF SOUTH CAROLINA   (United States)

^d UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033480324     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199903)14:2<153::AID-RSA3>3.3.CO;2-I     Document Type: Article

References (55)

1. R. Agarwala, V. Bafna, M. Farach, B. Narayanan, M. Paterson, and M. Thorup, On the approximability of numerical taxonomy: fitting distances by tree metrics, Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, 1996, pp. 365-372.
2. D.J. Aldous, "Probability distributions on cladograms," Discrete random structures, IMA Vol. in Mathematics and its Applications, Vol. 76, D.J. Aldous and R. Permantle (Editors), Springer-Verlag, Berlin/New York, 1995, pp. 1-18.
3. N. Alon and J.H. Spencer, The probabilistic method, Wiley, New York, 1992.
4. A. Ambainis, R. Desper, M. Farach, and S. Kannan, Nearly tight bounds on the learnability of evolution, Proc of the 1998 Foundations of Comp Sci, to appear.
5. K. Atteson, The performance of neighbor-joining algorithms of phylogeny reconstruction, Proc COCOON 1997, Computing and Combinatorics, Third Annual International Conference, Shanghai, China, Aug. 1997, Lecture Notes in Computer Science, Vol. 1276, Springer-Verlag, Berlin/New York, pp. 101-110.
6. H.-J. Bandelt and A. Dress, Reconstructing the shape of a tree from observed dissimilarity data, Adv Appl Math 7 (1986), 309-343.
7. V. Berry and O. Gascuel, Inferring evolutionary trees with strong combinatorial evidence, Proc COCOON 1997, Computing and Combinatorics, Third Annual International Conference, Shanghai, China, Aug. 1997, Lecture Notes in Computer Science, Vol. 1276, Springer-Verlag, Berlin/New York, pp. 111-123.
8. J.K.M. Brown, Probabilities of evolutionary trees, Syst Biol 43 (1994), 78-91.
9. D.J. Bryant and M.A. Steel, Extension operations on sets of leaf-labelled trees, Adv Appl Math 16 (1995), 425-453.
10. P. Buneman, "The recovery of trees from measures of dissimilarity," Mathematics in the archaeological and historical sciences, F.R. Hodson, D.G. Kendall, P. Tatu (Editors), Edinburgh Univ. Press, Edinburgh, 1971, pp. 387-395.
11. M. Carter, M. Hendy, D. Penny, L.A. Székely, and N.C. Wormald, On the distribution of lengths of evolutionary trees, SIAM J Disc Math 3 (1990), 38-47.
12. J.A. Cavender, Taxonomy with confidence, Math Biosci 40 (1978), 271-280.
13. J.T. Chang and J.A. Hartigan, Reconstruction of evolutionary trees from pairwise distributions on current species, Computing Science and Statistics: Proc 23rd Symp on the Interface, 1991, pp. 254-257.
14. H. Colonius and H.H. Schultze, Tree structure for proximity data, British J Math Stat Psychol 34 (1981), 167-180.
15. W.H.E. Day, Computational complexity of inferring phylogenies from dissimilarities matrices, Inform Process Lett 30 (1989), 215-220.
16. W.H.E. Day and D. Sankoff, Computational complexity of inferring phylogenies by compatibility, Syst Zoology 35 (1986), 224-229.
17. M.C.H. Dekker, Reconstruction methods for derivation trees, Master's Thesis, Vrije Universiteit, Amsterdam, 1986.
18. P. Erdos and A. Rényi, On a classical problem in probability theory, Magy Tud Akad Mat Kutató Int Közl 6 (1961), 215-220.
19. P.L. Erdos, M.A. Steel, L.A. Székely, and T. Warnow, Local quartet splits of a binary tree infer all quartet splits via one dyadic inference rule, Comput Artif Intell 16(2) (1997), 217-227.
20. P.L. Erdos, M.A. Steel, L.A. Székely, and T. Warnow, "Inferring big trees from short quartets," ICALP'97, 24th International Colloquium on Automata, Languages, and Programming (Silver Jubilee of EATCS), Bologna, Italy, July 7-11, 1997, Lecture Notes in Computer Science, Vol. 1256, Springer-Verlag, Berlin/New York, 1997, 1-11.
21. P.L. Erdos, M.A. Steel, L.A. Székely, and T. Warnow, A few logs suffice to build (almost) all trees-II, Theoret Comput Sci special issue on selected papers from ICALP 1997, to appear.
22. P.L. Erdos, K. Rice, M. Steel, L. Szekely, and T. Warnow, The short quartet method, Mathematical Modeling and Scientific Computing, to appear.
23. M. Farach and S. Kannan, Efficient algorithms for inverting evolution, Proc ACM Symp on the Foundations of Computer Science, 1996, pp. 230-236.
24. M. Farach, S. Kannan, and T. Warnow, A robust model for inferring optimal evolutionary trees, Algorithmica 13 (1995), 155-179.
25. J.S. Farris, A probability model for inferring evolutionary trees, Syst Zoology 22 (1973), 250-256.
26. J. Felsenstein, Cases in which parsimony or compatibility methods will be positively misleading, Syst Zoology 27 (1978), 401-410.
27. E.F. Harding, The probabilities of rooted tree shapes generated by random bifurcation, Adv Appl Probab 3 (1971), 44-77.
28. M.D. Hendy, The relationship between simple evolutionary tree models and observable sequence data, Syst Zoology 38(4) (1989), 310-321.
29. D. Hillis, Approaches for assessing phylogenetic accuracy, Syst Biol 44 (1995), 3-16.
30. D. Hillis, Inferring complex phylogenies, Nature 383(12) (Sept. 1996), 130-131.
31. D. Hillis, J. Huelsenbeck, and D. Swofford, Hobgoblin of phylogenetics? Nature 369 (1994), 363-364.
32. M. Hendy, C. Little, and D. Penny, Comparing trees with pendant vertices labelled, SIAM J Appl Math 44 (1984), 1054-1065.
33. J. Huelsenbeck, Performance of phylogenetic methods in simulation, Syst Biol 44 (1995), 17-48.
34. J.P. Huelsenbeck and D. Hillis, Success of phylogenetic methods in the four-taxon case, Syst Biol 42 (1993), 247-264.
35. S. Kannan, personal communication.
36. M. Kimura, Estimation of evolutionary distances between homologous nucleotide sequences, Proc Nat Acad Sci USA 78 (1981), 454-458.
37. J. Neyman, "Molecular studies of evolution: a source of novel statistical problems," Statistical decision theory and related topics, S.S. Gupta and J. Yackel (Editors), Academic Press, New York, 1971, pp. 1-27.
38. H. Philippe and E. Douzery, The pitfalls of molecular phylogeny based on four species, as illustrated by the cetacea/artiodactyla relationships, J Mammal Evol 2 (1994) 133-152.
39. K. Rice and T. Warnow, "Parsimony is hard to beat!," Proc COCOON 1997, Computing and combinatorics, Third Annual International Conference, Shanghai, China, Aug. 1997, Lecture Notes in Computer Science, Vol. 1276, Springer-Verlag, Berlin/New York, pp. 124-133.
40. N. Saitou and M. Nei, The neighbor-joining method: A new method for reconstructing phylogenetic trees, Mol Biol Evol 4 (1987), 406-425.
41. N. Saitou and T. Imanishi, Relative efficiencies of the Fitch-Mzargoliash, maximum parsimony, maximum likelihood, minimum evolution, and neighbor-joining methods of phylogenetic tree construction in obtaining the correct tree, Mol Biol Evol 6 (1989), 514-525.
42. Y.S. Smolensky, A method for linear recording of graphs, USSR Comput Math Phys 2 (1969), 396-397.
43. M.A. Steel, The complexity of reconstructing trees from qualitative characters and subtrees, J Classification 9 (1992), 91-116.
44. M.A. Steel, Recovering a tree from the leaf colourations it generates under a Markov model, Appl Math Lett 7 (1994), 19-24.
45. M.A. Steel, L.A. Székely, and P.L. Erdos, The number of nucleotide sites needed to accurately reconstruct large evolutionary trees, DIMACS Technical Report No. 96-19.
46. M.A. Steel, L.A. Székely, and M.D. Hendy, Reconstructing trees when sequence sites evolve at variable rates, J Comput Biol 1 (1994), 153-163.
47. K. Strimmer and A. von Haeseler, Quartet puzzling: a quartet maximum likelihood method for reconstructing tree topologies, Mol Biol Evol 13 (1996), 964-969.
48. K. Strimmer, N. Goldman, and A. von Haeseler, Bayesian probabilities and quartet puzzling, Mol Biol Evol 14 (1997), 210-211.
49. D.L. Swofford, G.J. Olsen, P.J. Waddell, and D.M. Hillis, "Phylogenetic inference," Molecular systematics, D.M. Hillis, C. Moritz, and B.K. Mable (Editors), Chap. 11, 2nd ed., Sinauer Associates, Inc., Sunderland, 1996, pp. 407-514.
50. N. Takezaki and M. Nei, Inconsistency of the maximum parsimony method when the rate of nucleotide substitution is constant, J Mol Evol 39 (1994), 210-218.
51. T. Warnow, Combinatorial algorithms for constructing phylogenetic trees, Ph.D. thesis, University of California-Berkeley, 1991.
52. P. Winkler, personal communication.
53. K.A. Zaretsky, Reconstruction of a tree from the distances between its pendant vertices, Uspekhi Math Nauk (Russian Math Surveys), 20 (1965), 90-92 (in Russian).
54. A. Zharkikh and W.H. Li, Inconsistency of the maximum-parsimony method: The case of five taxa with a molecular clock, Syst Biol 42 (1993), 113-125.
55. S.J. Wilson, Measuring inconsistency in phylogenetic trees, J Theoret Biol 190 (1998), 15-36.