Refined Buneman Trees

100000
90000
Performance of the refined Buneman tree algorithm
best fit
80000
70000
Running time (ms.)
60000
50000
40000
30000
20000
10000
0
4 8 16 32 64 128
Input size
Figure 15.1: The running time of the refined Buneman algorithm. Notice the
artifact at power of two intervals. This stems from the quad tree data structure
described in chapter 8
• Input stop size 174 1
• Number of repetitions 100
To analyse the asymptotic running time performance of the algorithm, the
test data was analysed using the nonlinear least-squares (NLLS) Marquardt-
Levenberg algorithm via the gnuplot ([gnu99]) fit command.
The expectation was that the performance of the algorithm would be O(n 3 ),
and therefore the fit-function was chosen to be f(x) = ax b . The fit of the
function f with the whole dataset (input sizes 4 – 174) returned the following
values: a =0.0130805 and b =3.02047. A plot of the data along with the
function f is shown in Figure 15.1. The figure shows a plot of the running time
in milliseconds against the input size in number of species.
Figure 15.1 shows an artifact from the implementation, namely a jump in
running time performance consistent with intervals matching powers of 2. This
artifact stems from the dimensioning of the quad tree data structure described in
1 Actually the stop size was 200, but after 3 consecutive days of running the test it was
halted due to impatience.
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