Refined Buneman Trees

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Quartet: 0 3 | 1 4 0.12353367495389822 Quartet: 0 3 | 2 2 0.6541561669265625 Quartet: 0 3 | 2 4 0.14876275841694736 Quartet: 0 3 | 4 4 0.4080878060278718 Quartet: 3 3 | 1 1 0.888989662949193 Quartet: 3 3 | 1 2 0.40577954477681416 Quartet: 3 3 | 1 4 0.5477608935480884 Quartet: 3 3 | 2 2 0.8431623196522158 Quartet: 3 3 | 2 4 0.49201563781250585 Quartet: 3 3 | 4 4 0.7513406854234302 Buneman Index: -0.12021742739037003 Split: 01110 Quartet: 0 0 | 1 1 0.13390431386278734 Quartet: 0 0 | 1 2 -0.11408473844105449 Quartet: 0 0 | 1 3 -0.3308581304922155 Quartet: 0 0 | 2 2 0.558519102302884 Quartet: 0 0 | 2 3 -0.09563706462367855 Quartet: 0 0 | 3 3 0.09336908810197464 Quartet: 0 4 | 1 1 0.2602544302024729 Quartet: 0 4 | 1 2 -0.16721043223432325 Quartet: 0 4 | 1 3 -0.2045080141525299 Quartet: 0 4 | 2 2 0.5053934085096152 Quartet: 0 4 | 2 3 -0.14876275841694736 Quartet: 0 4 | 3 3 0.34325287939555843 Quartet: 4 4 | 1 1 0.5448085612764465 Quartet: 4 4 | 1 2 0.11734369883965029 Quartet: 4 4 | 1 3 0.20357979187534186 Quartet: 4 4 | 2 2 0.6104717294506344 Quartet: 4 4 | 2 3 0.25932504761092445 Quartet: 4 4 | 3 3 0.7513406854234302 Buneman Index: -0.2676830723223727 Split: 01111 Quartet: 0 0 | 1 1 0.13390431386278734 Quartet: 0 0 | 1 2 -0.11408473844105449 Quartet: 0 0 | 1 3 -0.3308581304922155 Quartet: 0 0 | 1 4 -0.12635011633968557 Quartet: 0 0 | 2 2 0.558519102302884 Quartet: 0 0 | 2 3 -0.09563706462367855 Quartet: 0 0 | 2 4 0.05312569379326881 Quartet: 0 0 | 3 3 0.09336908810197464 Quartet: 0 0 | 3 4 -0.2498837912935838 Quartet: 0 0 | 4 4 0.15820401473428802 Buneman Index: -0.29037096089289965 Refined Buneman splits: 01000 0.1909466830833146 00100 0.39426472835755577 00010 0.1411876204138139 00001 0.11121100989033475 103
Appendix B Garbage Collector Log 0.000: [GC 511K->156K(1984K), 0.0090600 secs] 0.178: [GC 668K->154K(1984K), 0.0041940 secs] 0.241: [GC 666K->155K(1984K), 0.0020350 secs] 0.264: [GC 667K->196K(1984K), 0.0014720 secs] 0.277: [GC 708K->184K(1984K), 0.0011120 secs] 0.299: [GC 696K->158K(1984K), 0.0007900 secs] 0.310: [GC 670K->178K(1984K), 0.0006680 secs] 0.327: [GC 690K->164K(1984K), 0.0005610 secs] 0.340: [GC 676K->165K(1984K), 0.0009310 secs] 0.353: [GC 677K->166K(1984K), 0.0006800 secs] 0.363: [GC 678K->166K(1984K), 0.0005850 secs] 0.373: [GC 678K->167K(1984K), 0.0006100 secs] 0.384: [GC 679K->168K(1984K), 0.0006100 secs] 0.397: [GC 680K->212K(1984K), 0.0010710 secs] 0.408: [GC 724K->168K(1984K), 0.0007290 secs] 0.419: [GC 680K->175K(1984K), 0.0005970 secs] 0.429: [GC 687K->183K(1984K), 0.0006870 secs] 0.438: [GC 695K->196K(1984K), 0.0006830 secs] 0.453: [GC 708K->183K(1984K), 0.0007270 secs] 0.461: [GC 695K->246K(1984K), 0.0014170 secs] 0.475: [GC 758K->304K(1984K), 0.0027140 secs] 0.485: [GC 816K->363K(1984K), 0.0026530 secs] 0.501: [GC 875K->312K(1984K), 0.0006540 secs] 0.511: [GC 824K->311K(1984K), 0.0004770 secs] 0.523: [GC 823K->320K(1984K), 0.0006030 secs] 0.532: [GC 832K->319K(1984K), 0.0006790 secs] 0.544: [GC 831K->329K(1984K), 0.0008010 secs] 0.553: [GC 841K->328K(1984K), 0.0007290 secs] 0.565: [GC 840K->331K(1984K), 0.0009070 secs] 0.576: [GC 843K->329K(1984K), 0.0007710 secs] 0.584: [GC 841K->456K(1984K), 0.0028120 secs] 0.599: [GC 968K->464K(1984K), 0.0020600 secs] 0.609: [GC 976K->464K(1984K), 0.0018370 secs] 0.623: [GC 976K->479K(1984K), 0.0005670 secs] 0.631: [GC 991K->477K(1984K), 0.0005740 secs] 0.640: [GC 989K->614K(1984K), 0.0028960 secs] 0.655: [GC 1126K->627K(1984K), 0.0020690 secs] 0.666: [GC 1139K->627K(1984K), 0.0018740 secs] 0.676: [GC 1139K->813K(1984K), 0.0037820 secs] 0.695: [GC 1325K->786K(1984K), 0.0016900 secs] 0.705: [GC 1298K->787K(1984K), 0.0010740 secs] 0.718: [GC 1299K->801K(1984K), 0.0006760 secs] 0.727: [GC 1313K->801K(1984K), 0.0006270 secs] 0.736: [GC 1313K->801K(1984K), 0.0006380 secs] 0.749: [GC 1313K->811K(1984K), 0.0007980 secs] 0.757: [GC 1323K->811K(1984K), 0.0008100 secs] 0.766: [GC 1323K->812K(1984K), 0.0007680 secs] 0.780: [GC 1324K->813K(1984K), 0.0008510 secs] 0.788: [GC 1325K->812K(1984K), 0.0008660 secs] 0.799: [GC 1324K->812K(1984K), 0.0007680 secs] 0.808: [GC 1324K->1006K(1984K), 0.0047390 secs] 0.830: [GC 1518K->971K(1984K), 0.0012210 secs] 0.839: [GC 1483K->971K(1984K), 0.0007970 secs] 0.847: [GC 1483K->1068K(1984K), 0.0021650 secs] 0.864: [GC 1580K->1142K(1984K), 0.0033550 secs] 0.875: [GC 1654K->1144K(1984K), 0.0024180 secs] 0.886: [GC 1656K->1144K(1984K), 0.0005500 secs] 0.900: [GC 1656K->1162K(1984K), 0.0007140 secs] 0.908: [GC 1674K->1162K(1984K), 0.0007450 secs] 0.917: [GC 1674K->1161K(1984K), 0.0007530 secs] 0.936: [GC 1673K->1163K(1984K), 0.0018910 secs] 104
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Refined Buneman Trees Lasse Westh-N
Page 3 and 4:
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
Page 9 and 10:
The theory of evolution has also be
Page 11 and 12:
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
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time in the algorithm. In [BFÖ+ 03
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Figure 3.1: A tree of life. 22
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knowing its origins, but how does h
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anging from huge time complexity to
Page 29 and 30:
Algorithm 2 The Neighbor-Joining al
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A, C, T 1 2 3 T A, C, T T C, T A, T
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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
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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 and 72: implementing an algorithm with a hi
Page 73 and 74: Chapter 12 Source Code The source c
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: Quartet: 0 0 | 1 4 -0.1263501163396
Page 107 and 108: Bibliography [AJL + 02] Bruce Alber
Page 109: [Kim80] M. Kimura. A simple model f
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