computing the quartet distance between general trees

More documents

Recommendations

Info

60 CHAPTER 8. RESULTS AND DISCUSSIONfaster for trees with less than 200 leaves.A general observation based on the experiments with the three algorithms is thateven though their respective time complexities are only defined in terms of the inputsize n, this does not mean that the implementations are not sensitive to the structure ofthe input, e.g. the degree of the internal nodes.8.1 Large numbersOne thing not mentioned, but important to every quartet distance algorithm, is the needof handling large numbers. Quartet distance results can often be very large, simply becausethere are such a large amount of quartets to compare. As an example, 600 leavesresult in ( 600) 4 = 5346164850 distinct quartets to compare, which is a number exceedingthe capacity of a normal 32 bit integer. Thus, if many of those quartets inherit a differenttopology in the two trees, there is a risk that the result will overflow. Therefore, thisshould be taken into consideration, when implementing a quartet distance algorithm –which size of trees are to be compared and which architecture will be used.Python provides a transparent handling of large numbers, which will be enough foralgorithms like the cubic and quartic algorithms. However, when utilizing external routines,which was the case with BLAS matrix multiplication, in the sub-cubic algorithm,special care must be taken and the right data structures used.This means that pure C++ implementations, without special libraries for large numbers,are limited by the architecture but pure Python implementations are not. In anycase, external procedures may giver further restrictions.
8.1. LARGE NUMBERS 61time in seconds - t(n)10000100010010Comparison of the three algorithms, Python implementation.sub-cubic algorithmcubic algorithmquartic algorithmn 2n 3n 410.150 100 200 500 800number of leaves - nFigure 8.1: Comparison of the performances of the three algorithms implementedin Python.time in seconds - t(n)1000100101Comparison of the three algorithms, C++ implementation.sub-cubic algorithmcubic algorithmquartic algorithmn 2n 3n 40.10.0150 100 200 500 800number of leaves - nFigure 8.2: Comparison of the performances of the three algorithms implementedin C++.
Page 1:
Master’s thesisCOMPUTING THE QUAR
Page 5:
AcknowledgementsFirst of all I woul
Page 8 and 9:
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
Page 14 and 15:
6 CHAPTER 1. INTRODUCTIONsub-cubic
Page 17 and 18: Chapter 2PrerequisitesFirst, this c
Page 19: 2.2. CHOICE OF LANGUAGE AND TEST EN
Page 22 and 23: 14 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 71 and 72: Chapter 9ConclusionThe focus of thi
Page 73 and 74: Bibliography[1] Mukul S. Bansal, Ji
Page 75: BIBLIOGRAPHY 67[20] M.S. Waterman a
Page 78 and 79: 70 APPENDIX A. PREPROCESSING FOR TH
Page 81 and 82: Appendix CReal-life application of
Page 83: 75t29t25t54t20t27 t13 t1t3t17t24t41
show all

computing the quartet distance between general trees

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?