By Jon Kleinberg, Éva Tardos

ISBN-10: 0321295358

ISBN-13: 9780321295354

* Algorithm layout * introduces algorithms by means of taking a look at the real-world difficulties that inspire them. The booklet teaches scholars a number of layout and research options for difficulties that come up in computing functions. The textual content encourages an realizing of the set of rules layout procedure and an appreciation of the function of algorithms within the broader box of desktop science.

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Maximum likelihood and minimum-steps methods for estimating evolutionary trees from data on discrete characters. Syst. Zool. 22(3), 240–249 (1973) 23. : Parsomony in systematics: biological and statistical issues. Annu. Rev. Ecol. Syst. 14, 313–333 (1983) 24. : Toward defining the course of evolution: minimum changes for a specific tree topology. Syst. Zool. 20, 406–416 (1971) 25. : Evolutionary trees with minimum nucleotide replacements from amino acid sequences. J. Mol. Evol. 3(4), 263–278 (1974) 26.

Theorem 2 In the general parsimony problem with F = R and d(x, y) = (y − x)2 , the subtree weight functions are quadratic. 3) with some parameters αu , φu , μu ∈ R. 4b) where βv is defined for all v ∈ V by βv = 1 αv αv +1 if v is a leaf; otherwise. 4c) By Theorem 2, A NCESTRAL can proceed by storing α and μ at every node. 3 Ancestral Inference by Parsimony 37 Theorem 3 For squared parsimony, algorithms A NCESTRAL and L ABELING compute an optimal labeling in O(m) time and O(m) space. 4c) in O(m) total time.

J. Evol. Biol. 23(1), 53–71 (2010) 28. : Reconstructing the history and geography of an evolutionary tree. Am. Math. Mon. 79(6), 596–603 (1972) 29. : Properties of phylogenetic trees generated by Yule-type speciation models. Math. Biosci. 170(1), 91 (2001) 30. : Vorlesungen über die Theorie der Polyeder. Springer, Berlin (1934) 31. : Entanglement invariants and phylogenetic branching. J. Math. Biol. 51(1), 18–36 (2005) 32. : Isolation by distance. Genetics 28(2), 114–138 (1943) Chapter 3 How to Infer Ancestral Genome Features by Parsimony: Dynamic Programming over an Evolutionary Tree Miklós Csurös ˝ Abstract We review mathematical and algorithmic problems of reconstructing evolutionary features at ancestors in a known phylogeny.

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