computing the quartet distance between general trees

More documents

Recommendations

Info

22 CHAPTER 4. QUARTIC TIME ALGORITHMThis evidence makes it clear that it is in fact a worst-case quartic algorithm. In addition,the figure also reveals the interrelationship between the five groups of data. Observe thatthere is a rather large difference in running time, with the star tree being the faster andthe binary tree being the slower one to deal with. This seems natural, since the internalstructures of the trees are very different. The traversal of a tree with a complex internalstructure, a large number of internal nodes, is more time consuming and since the algorithmis based on a large number of traversals, this penalty is observable in the plots.And of course, the time bound is related to the number of leaves and not the internalstructure of the trees.This algorithm has shown – not surprisingly – to be very slow and not competitivewith a sub-cubic algorithm. It has merely worked as a reference of correctness, whenimplementing the other algorithms. Nevertheless, in Chapter 8, where all the results ofthis thesis are compared and discussed, the practical performance is compared to thoseof the other algorithms.
4.1. IMPLEMENTATION 23time in seconds - t(n)100001000100101bin, best exp= 3.93ran, best exp= 3.84sqrt, best exp= 3.69star, best exp= 3.65wc, best exp= 3.69n 3n 4n 5Python implementation of the quartic algorithm.0.10.0110 50 100 200number of leaves - nFigure 4.2: Performance of the quartic algorithm implemented in Python.time in seconds - t(n)1000010001001010.1bin, best exp= 3.81ran, best exp= 3.71sqrt, best exp= 3.37star, best exp= 3.27wc, best exp= 3.44n 3n 4n 5C++ implementation of the quartic algorithm.0.0110 50 100 200number of leaves - nFigure 4.3: Performance of the quartic algorithm implemented in 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 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 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?