Refined Buneman Trees

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Algorithm 7 The DISCARD-RIGHT algorithm Require: σ = U 1 |V 1 and σ ′ = U 2 |V 2 are incompatible splits. Ensure: return true if μ σ ′ ≤ 0, false otherwise. 1: A = U1 ∩ U2, B = U1 ∩ V 2, C = V 1 ∩ U2, D = V 1 ∩ V 2 2: Q = ∅ 3: for a =1to|A| do 4: for b =1to|B| do 5: for c =1to|C| do 6: for d =1to|D| do 7: determine permutations q 1 and q 2 of A[a], B[b], C[c] andD[d] such that q 1 ∈ q(σ) andq 2 ∈ q(σ ′ ) 8: Q = Q ∪ q 2 9: if |Q| = n − 3 then 10: goto sum 11: end if 12: end for 13: end for 14: end for 15: end for 16: sum: 17: if ∑ n−3 i=1 β Q[i] ≤ 0 then 18: return TRUE 19: end if 20: return FALSE 63
Chapter 10 The Selection Algorithm In Algorithm 4 we are faced with the problem of removing the (n − 3) largest elements from a set of size 3(n−3) or more. In general, the problem is removing the i largest elements from a set A of size n, wherei
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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
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
Page 61 and 62: 30000 Quad Tree performance charact
Page 63: sets A, B, C and D by scanning the
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 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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