computing the quartet distance between general trees

Chapter 8Results and discussionThe experiments with each of the three algorithms have been commented separately inChap. 4, 6 and 7. The general impression has been positive: the quartic and cubic algorithmswere indeed performing within – and also rather close to – the expected timebounds, however, the quartic algorithm was more sensitive to the variations in inputdata. The implementation of the sub-cubic algorithm has not been precisely followingthe theoretic guidelines and as a consequence some compromises have been introduced.More precisely, experimental verification made it clear that padding the matricesto square matrices did not give an advantage over the normal multiplication. Nevertheless,the final implementation has been thoroughly tested with different input – in anattempt of finding the worst possible input – and the result is an algorithm that behavessub-cubicly in every situation. However, while the algorithm shows a sub-cubic performancefor all types of trees presented, both the actual running time and the developmentin time-usage is clearly varying between trees. Hence, the star tree has an interesting role.For the size of trees used in this thesis (≤ 800 leaves), the star tree is both the fastest todeal with and the tree that makes the algorithm show the worst development in timeusage.As a consequence, I find it natural to assume that running time of the sub-cubicalgorithm on the star tree, and to some extent also the wc tree, will continue growingfaster than on the other inputs and eventually, on much larger trees, the star trees will bethe most time consuming inputs to deal with.The final result of the experiments was briefly revealed and commented rather cursoryin Chap. 1 but shown again in Fig. 8.1 and Fig. 8.2. The two figures compare theexperimental results of the three algorithms implemented in Python and C++ respectively.These plots are clear evidence that the sub-cubic algorithm does not only meetthe theoretic expectations but it is faster in practice as well. The C++ implementation isfaster for trees with 80 leaves and more while the Python implementation is not clearly59