Refined Buneman Trees

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The interface has two methods that need to be implemented. Firstly, we would have to implement the method isApplicable which takes two parameters, a list of taxa (names of species) and a set of distance data (in the form of a matrix). The point is not to test if our algorithm can accept this type of input, we know that already since we are implementing the Distances2Splits interface. Instead, the method is designed to test the quality of the input. Our refined Buneman tree algorithm requires a minimum input size of four, for example. So in case the input data is not we will say that we cannot handle the data, and JSplits can then use that information to ensure our algorithm will never have to be computed with this input. JSplits handles this by blanking out the drop down menu option for our algorithm. Secondly, we have to implement the apply method. We are given the same parameters as before, and we are required to return a set of splits. JSplits can use these splits to create a graphical representation of the refined Buneman tree. The author has placed all source code in a separate package so as to not pollute the JSplits directory structure with irrelevant files. The apply method basically only performs translation from the (oddly indexed) JSplits data to simple distance matrix with the type double[][]. This simple matrix is then passed to the real implementation in the seperate package, which is an implementation of the following interface. We simply ignore the taxa list for now. package dk.birc.rbt; interface Distances2SplitsAlgorithmInterface { Split[] compute(double[][] distanceMatrix); } The Split class thus returned has the following type: package dk.birc.rbt; class Split { boolean[] split; } double weight; Finally the array of splits is translated into a set of splits in the JSplits sense, which basically involves re-indexing and adding taxa names, and that set is returned. 71
Chapter 12 Source Code The source code for the implementation described in the previous chapters is available from the following webpage. As the implementation has been done in Java, the implementation should be able to run on any machine of any architecture using any operating system, provided a Java Runtime Environment (JRE) is available. http://www.daimi.au.dk/~lasse/thesis/ The Java source code files are available for browsing online, and for downloading in a Zip file. The code is packaged 1 in two directory structures: dk.birc.rbt contains source code for the implementation of the refined Buneman tree algorithm. The code is modularized into one .java file for each Java class for a total of 31 source files, containing roughly 2600 lines of code. splits.algorithms.distances contains the plugin code that adapts the refined Buneman method to the JSplits software package. Basically this consists of one file which performs simple transformations between the formats in JSplits and in the refined Buneman implementation. All Java classes and methods have been decorated using the Javadoc format ([Sun03]), and thus a Javadoc documentation of the source code tree is available for online browsing, using the webpage mentioned above. The implementation has furthermore been documented in a series of UML diagrams, also available from the webpage, in PostScript format. The UML diagrams are generally too large to fit on A4 paper, therefore they have not been included in this thesis. These diagrams should convey an overview of the implementation. 1 packaged in the Java sense: using a reverse domain name scheme should generate a unique namespace, and the directory structure follows the package name with ’.’ replaced by ’/’ 72
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Refined Buneman Trees Lasse Westh-N
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This thesis is dedicated to my fami
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Contents 1 Introduction 7 1.1 Docum
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13.3 Correctness of the reference i
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The theory of evolution has also be
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Chapter 2 Definitions This chapter
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A C B Figure 2.1: An evolutionary t
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2.4 Quartets To every set of four s
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2.6 Splits The partition of a finit
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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
Page 61 and 62: 30000 Quad Tree performance charact
Page 63 and 64: sets A, B, C and D by scanning the
Page 65 and 66: Chapter 10 The Selection Algorithm
Page 67 and 68: is O(n 2 ). The algorithm uses a di
Page 69 and 70: Chapter 11 JSplits Figure 11.1: A s
Page 71: implementing an algorithm with a hi
Page 75 and 76: Chapter 13 The Reference Implementa
Page 77 and 78: • the splits that are generated.
Page 79 and 80: Chapter 14 Correctness This chapter
Page 81 and 82: The best possible way of testing wo
Page 83 and 84: 100000 90000 Performance of the ref
Page 85 and 86: of the size of the heap during the
Page 87 and 88: 140000 Space complexity best fit: x
Page 89 and 90: Chapter 16 Comparing Evolutionary T
Page 91 and 92: Figure 16.1: The size of the set B(
Page 93 and 94: Figure 16.2: The total number of sp
Page 95 and 96: that it over-induces splits, and th
Page 97 and 98: efined Buneman therefore suffers a
Page 99 and 100: Speedups might be achieved using op
Page 101 and 102: Appendix A Correctness of the Refer
Page 103 and 104: Quartet: 0 0 | 1 4 -0.1263501163396
Page 105 and 106: Appendix B Garbage Collector Log 0.
Page 107 and 108: Bibliography [AJL + 02] Bruce Alber
Page 109: [Kim80] M. Kimura. A simple model f
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