computing the quartet distance between general trees

Chapter 3Experimental approachAlgorithms for computing the quartet distance should all produce the same simple result,namely a single number. Once confidence in one algorithm has been established,it is rather simple to verify another such algorithm and build the same level of trust inthe correctness of its results. That is one reason for implementing several different algorithmsalong with each other, and so is a strong motivation for the inclusion of thequartic algorithm of Chap. 4, because it is simple and therefore easy to verify by hand.And thorough verification has indeed been practiced, with various small examples andunit tests.Another way to gain trust, is of course to rely on some independent implementation.This has also been done in the effort to cement the correctness of my work. A piece ofsoftware called QDist, described in Mailund and Pedersen [13] has been utilized. It isan implementation of the O(n log 2 n) algorithm presented in Brodal et al. [2], which isworking only on binary trees. However, since there was no working software for generaltrees at hand, all results involving general trees had to be verified separately.After implementing three algorithms using completely different approaches, in twodifferent programming languages, my confidence in the correctness is very high.Needless it is to say that correctness of the result is essential, but yet another allimportantproperty is the running time. Especially to this thesis, where running timeis the quality measure, by which the algorithms are compared. Experiments are usedto determine the running time of each algorithm, as to verify whether the theoreticalpromised time bounds are correct, assess the practical behaviour of the algorithms, whichmight be different than anticipated, and last, to be able to compare the algorithms againstone another. For these experiments, a wide range of test data has been used. This isexplained in detail in the following Sec. 3.1. Other details about each experiment, e.g.which input trees have been used and how many times an experiment has been exe-13