Refined Buneman Trees

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Part I Overview of Evolutionary <strong>Trees</strong> 9
Chapter 2 Definitions This chapter is concerned with defining the terms used throughout the text, and their relation. The definitions are largely copied from [BFÖ+ 03], but with some additional comments. 2.1 Species Species — a set of animals or plants in which the members have similar characteristics to each other and can breed with each other. From Cambridge Advanced Learners Dictionary In this text we shall use the term species more loosely than the definition above suggests. The term is taken from a bioinformatics context, but it should be understood to mean more than just plants or animals. In his original paper [Bun71], Peter <strong>Buneman</strong> was concerned with both biology and filiation of manuscripts. But we are basically interested in anything which is related by some evolutionary relationship or phylogeny. We can indeed compare apples and oranges, however it makes no sense to compare species of fish to editions of Hamlet. Thus, for our purposes we shall define the a set of species to mean something along the lines of a set of objects in which the members have a measurable phylogeny. In the following we will need to refer to the first k species from a set of species X = {x 1 , ··· ,x n } assuming some arbitrary ordering, so we define for integers k ∈{1, ··· ,n},X k = {x 1 , ··· ,x k }. 2.2 Evolutionary tree Definition 1 of an evolutionary tree is taken from [SS03], it is a bit more elaborate than the equivalent definition in [BFÖ+ 03]. The idea of the evolutionary tree is, in the words of Semple & Steel ([SS03]) to provide a standard graphical 10
Page 1 and 2: Refined Buneman Trees Lasse Westh-N
Page 3 and 4: This thesis is dedicated to my fami
Page 5 and 6: Contents 1 Introduction 7 1.1 Docum
Page 7 and 8: 13.3 Correctness of the reference i
Page 9: The theory of evolution has also be
Page 13 and 14: A C B Figure 2.1: An evolutionary t
Page 15 and 16: 2.4 Quartets To every set of four s
Page 17 and 18: 2.6 Splits The partition of a finit
Page 19 and 20: evolutionary tree gives an invaluab
Page 21 and 22: time in the algorithm. In [BFÖ+ 03
Page 23 and 24: Figure 3.1: A tree of life. 22
Page 25 and 26: knowing its origins, but how does h
Page 27 and 28: anging from huge time complexity to
Page 29 and 30: Algorithm 2 The Neighbor-Joining al
Page 31 and 32: A, C, T 1 2 3 T A, C, T T C, T A, T
Page 33 and 34: Part II Implementing Refined Bunema
Page 35 and 36: Algorithm 3 Overapproximating the r
Page 37 and 38: the pseudo-code for the algorithm i
Page 39 and 40: AE DE D B e E BC A C BE AC Figure 5
Page 41 and 42: construction, but we still have to
Page 43 and 44: Chapter 6 TheTreeDataStructure This
Page 45 and 46: incidentedge Figure 6.2: The world
Page 47 and 48: interface EdgeIterator { boolean ha
Page 49 and 50: Figure 6.7: An example a node which
Page 51 and 52: So how do we find σ ′ We start
Page 53 and 54: Algorithm 5. Offhand, the algorithm
Page 55 and 56: Algorithm 6 The algorithm that calc
Page 57 and 58: a b c d root ab cd Figure 8.2: Upda
Page 59 and 60: 6000 Quad Tree performance characte
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30000 Quad Tree performance charact
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sets A, B, C and D by scanning the
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Chapter 10 The Selection Algorithm
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is O(n 2 ). The algorithm uses a di
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Chapter 11 JSplits Figure 11.1: A s
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implementing an algorithm with a hi
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Chapter 12 Source Code The source c
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Chapter 13 The Reference Implementa
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• the splits that are generated.
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Chapter 14 Correctness This chapter
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The best possible way of testing wo
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100000 90000 Performance of the ref
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of the size of the heap during the
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140000 Space complexity best fit: x
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Chapter 16 Comparing Evolutionary T
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Figure 16.1: The size of the set B(
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Figure 16.2: The total number of sp
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that it over-induces splits, and th
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efined Buneman therefore suffers a
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Speedups might be achieved using op
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Appendix A Correctness of the Refer
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Quartet: 0 0 | 1 4 -0.1263501163396
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Appendix B Garbage Collector Log 0.
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Bibliography [AJL + 02] Bruce Alber
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[Kim80] M. Kimura. A simple model f
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