Refined Buneman Trees

• the splits that are generated.
• the quartets that are generated for each split.
• the Buneman scores for the quartets.
• the Buneman Index for each split.
• the weighted splits reported by the algorithm.
After running the test program it is then possible to study the output from
the program and ensure:
• all unique splits of size n are generated, i.e. all possible splits on the form
0xxx.
• all quartets ab|cd are generated such that a, b ∈ U, c, d ∈ V , a ≤ b and
c ≤ d.
• for each quartet q generated, β q (δ) is calculated correctly.
• for each split σ generated, μ σ (δ) is calculated correctly.
• the weighted splits reported by the algorithm all have positive refined
Buneman index, and all splits generated that have positive refined Buneman
index are reported.
Of course, this process is quite infeasible for larger δ, but the author has
read through outputs from a few runs, and has found no errors. The author
therefore concludes that the reference implementation is correct. An example
of such an output is given in appendix A.
13.4 Performance of the reference implementation
The performance characteristic for the algorithm can be seen in Figure 13.1.
The plots shows running time for input sizes 4–20. Clearly, it is infeasible to
run this implementation on large examples, but for our testing purposes it is
adequate.
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