computing the quartet distance between general trees

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.