computing the quartet distance between general trees

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6 CHAPTER 1. INTRODUCTIONsub-cubic and actually close to quadratic. Now the final result has briefly been revealedas an appetizer and I hope that will encourage the reader to seek the answers to why andhow, in the subsequent chapters.100001000Comparison of the three algorithms, Python implementation.sub-cubic algorithmcubic algorithmquartic algorithmn 2n 3n 4 50 100 200 500 800time in seconds - t(n)1001010.150 100 200 500 800number of leaves - ntime in seconds - t(n)1000100101Comparison of the three algorithms, C++ implementation.sub-cubic algorithmcubic algorithmquartic algorithmn 2n 3n 40.10.01number of leaves - nFigure 1.4: The final result of the experimental work of this thesis. See Chap.8 for more details.1.4 Focus of the thesisThe aim of this thesis is to explore in detail the practical behaviour of the theoretical subcubicalgorithm. Furthermore, I want to give readers who have no knowledge of quartetdistance calculation on general trees a gentle introduction to the subject. Therefore Iwill make an effort to explain everything thoroughly on the fly and not leave anythingunanswered. By continuously explaining my reasoning and immediately following upon the theory with implementation details and experimental results, I will encouragethe reader to go on and read everything chronologically. This will especially apply to themiddle part of the thesis, where I will deal with the algorithms one at a time, first theory,then implementation details and finally the results. Where appropriate, the thesis willfollow my workflow as to reflect the iterative process of my work to reveal every interest-
1.5. THESIS OUTLINE 7ing experience I had during the process.As mentioned, the thesis will focus on algorithmics and not the bioinformatics. Thepurpose is to explore the behaviour of three algorithms. This means that I will acceptthe theory as presented, try to verify the results through experiments and, in case of anysurprises, take a closer look at the algorithms to verify and possibly adjust the theory.Along the way, I will strive to provide enough information for the reader to reproduce theexperiments.1.5 Thesis outlineThe thesis is structured as follows. Chapter 2, Prerequisites, will go through terminologynecessary to prepare for the algorithmic chapters, and motivate the choice of implementationlanguages and experimental platforms. Chapter 3, Experimental approach, is ageneral explanation of how experiments are used to verify the quality of the implementationsand what kind of data is used for this purpose.Chapters 4 through 7 make up the algorithmic core of the thesis. Chapter 4 deals witheverything concerning the O(n 4 ) algorithm, which will also be referred to as the quarticalgorithm. Chapter 5 gives the details about an algorithmic concept called leaf set sizesthat is part of the cubic and sub-cubic algorithms which are the subjects of Chap. 6 andChap. 7 respectively, the latter of course being the more exhaustive.Chapter 8, Results and discussion, will put the results into perspective by comparingthe three algorithms and give an outline of my contributions and of what has beensuccessful and what has not. Finally, Chap. 9 will be a short overview and conclusion,summarizing the results and contributions, and a comment on possible future work.The appendices will contain: Appendix A, algorithmic details that do not fit in themain text, App. B, instructions on how to obtain and run the programs and finally App. C,a report on a real-life application of the final sub-cubic algorithm.
Page 1: Master’s thesisCOMPUTING THE QUAR
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Page 8 and 9: viiiCONTENTS5.3 Implementing leaf s
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7.2. IMPLEMENTATION 57ble sort, wil
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60 CHAPTER 8. RESULTS AND DISCUSSIO
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Chapter 9ConclusionThe focus of thi
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Bibliography[1] Mukul S. Bansal, Ji
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BIBLIOGRAPHY 67[20] M.S. Waterman a
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70 APPENDIX A. PREPROCESSING FOR TH
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Appendix CReal-life application of
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75t29t25t54t20t27 t13 t1t3t17t24t41
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