computing the quartet distance between general trees

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66 BIBLIOGRAPHY[9] Brian W. Davis, Gang Li, and William J. Murphy. Supermatrix and species tree methodsresolve phylogenetic relationships within the big cats, panthera (carnivora: Felidae).Molecular Phylogenetics and Evolution, 56(1):64 – 76, 2010. ISSN 1055-7903.doi: DOI:10.1016/j.ympev.2010.01.036.[10] William H. E. Day. Optimal algorithms for comparing trees with labeled leaves. Journalof Classification, 2:7–28, 1985. ISSN 0176-4268. 10.1007/BF01908061.[11] Annette Dobson. Comparing the shapes of trees. In Anne Street and Walter Wallis,editors, Combinatorial Mathematics III, volume 452 of Lecture Notes in Mathematics,pages 95–100. Springer Berlin / Heidelberg, 1975. 10.1007/BFb0069548.[12] George F. Estabrook, F. R. McMorris, and Christopher A. Meacham. Comparison ofundirected phylogenetic trees based on subtrees of four evolutionary units. SystematicZoology, 34(2):193–200, 1985. ISSN 00397989.[13] Thomas Mailund and Christian N. S. Pedersen. QDist-quartet distance betweenevolutionary trees. Bioinformatics, 20(10):1636–1637, 2004.[14] Thomas Mailund, Jesper Nielsen, and Christian N. S. Pedersen. A sub-cubic timealgorithm for computing the quartet distance between two general trees. In InternationalJoint Conferences on Bioinformatics, Systems Biology and Intelligent Computing(IJCBS), pages 565–568, 2009.[15] D. F. Robinson and L. R. Foulds. Comparison of phylogenetic trees. MathematicalBiosciences, 53(1-2):131–147, 1981. ISSN 0025-5564.[16] Mike A. Steel and David Penny. Distributions of tree comparison metrics-some newresults. Systematic Biology, 42(2):pp. 126–141, 1993. ISSN 10635157.[17] Martin Stig Stissing, Christian N. S. Pedersen, Thomas Mailund, Gerth Stølting Brodal,and Rolf Fagerberg. Computing the quartet distance between evolutionarytrees of bounded degree. In Series on Advances in Bioinformatics and ComputationalBiology, volume 5, pages 101–110, 2007.[18] Volker Strassen. Gaussian elimination is not optimal. Numerische Mathematik, 13:354–356, 1969. ISSN 0029-599X.[19] John Tsang. An approximation algorithm for character compatibility and fastquartet-based phylogenetic tree comparison. Master’s thesis, University of Waterloo,October 2000.
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Page 1:
Master’s thesisCOMPUTING THE QUAR
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AcknowledgementsFirst of all I woul
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viiiCONTENTS5.3 Implementing leaf s
Page 10 and 11:
2 CHAPTER 1. INTRODUCTIONhas is cal
Page 12 and 13:
4 CHAPTER 1. INTRODUCTIONIt is evid
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6 CHAPTER 1. INTRODUCTIONsub-cubic
Page 17 and 18:
Chapter 2PrerequisitesFirst, this c
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2.2. CHOICE OF LANGUAGE AND TEST EN
Page 22 and 23:
14 CHAPTER 3. EXPERIMENTAL APPROACH
Page 24 and 25: 16 CHAPTER 3. EXPERIMENTAL APPROACH
Page 26 and 27: 18 CHAPTER 3. EXPERIMENTAL APPROACH
Page 28 and 29: 20 CHAPTER 4. QUARTIC TIME ALGORITH
Page 30 and 31: 22 CHAPTER 4. QUARTIC TIME ALGORITH
Page 33 and 34: Chapter 5Calculating leaf set sizes
Page 35 and 36: 5.3. IMPLEMENTING LEAF SET ALGORITH
Page 37 and 38: 5.3. IMPLEMENTING LEAF SET ALGORITH
Page 39 and 40: Chapter 6Cubic time algorithmHere I
Page 41 and 42: 6.1. IMPLEMENTATION 33that we can l
Page 43 and 44: 6.1. IMPLEMENTATION 35carried out o
Page 45 and 46: Chapter 7Sub-cubic time algorithmIn
Page 47 and 48: 7.1. THE ALGORITHM 39CcabADFigure 7
Page 49 and 50: 7.1. THE ALGORITHM 41reflecting Eq.
Page 51 and 52: 7.1. THE ALGORITHM 43choice of indi
Page 53 and 54: 7.1. THE ALGORITHM 45More interesti
Page 55 and 56: 7.2. IMPLEMENTATION 477.2 Implement
Page 57 and 58: 7.2. IMPLEMENTATION 49tween the num
Page 59 and 60: 7.2. IMPLEMENTATION 51oretic approa
Page 61 and 62: 7.2. IMPLEMENTATION 53well. My impl
Page 63 and 64: 7.2. IMPLEMENTATION 55Performance o
Page 65: 7.2. IMPLEMENTATION 57ble sort, wil
Page 68 and 69: 60 CHAPTER 8. RESULTS AND DISCUSSIO
Page 71 and 72: Chapter 9ConclusionThe focus of thi
Page 73: Bibliography[1] Mukul S. Bansal, Ji
Page 78 and 79: 70 APPENDIX A. PREPROCESSING FOR TH
Page 81 and 82: Appendix CReal-life application of
Page 83: 75t29t25t54t20t27 t13 t1t3t17t24t41
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