Refined Buneman Trees

Chapter 15
Complexity
This chapter deals with the time and space complexity of the RBT-algorithm.
Before the advent of [BFÖ+ 03], a non-trivial algorithm for computing the RBT
did exist ([BB99]), but with a running time of O(n 5 ) and space consumption
O(n 4 ). The goals of [BFÖ+ 03] was to reduce these factors and make RBTs
computationally competitive to methods based on neighbor joining and on plain
Buneman trees, and in turn one of the goals of this thesis is to implement this
algorithm and demonstrate how RBTs can be used in practice. Therefore we
need to demonstrate that the implementation does indeed run in time O(n 3 )
and space O(n 2 ).
15.1 Running time
To analyse the running time of the algorithm the author has written the test
program which is parameterized by starting input size, ending input size and
number of repetitions per input size. The test program measures the running
time of the refined Buneman treee algorithm found by measuring the system
time before and after each computation of the algorithm, excluding the initialization
of a random input matrix. Input size and running time is reported for
each repetition.
The timing is not optimal; the running time does not reflect the exact running
time of the algorithm, since the algorithm does not run exclusively on the
test PC. However, the author made sure that the test PC was largely unused
during testing, meaning that no users and only a few system processes were
running during the time trials. Therefore the timing data might show a slightly
skewed picture of the running time, but very importantly, the skew is evenly
distributed and thus does not affect the test goal, with is to determine the
asymptotic running time behaviour of the algorithm.
The test was run with the following parameters:
• Input start size 4
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