A Simple Solution?

The trivial solution to the phylogeny problem would be to enumerate over all possible trees and calculate the target function for each one. However, the number of non-isomorphic, labeled, binary, rooted trees containing n leaves, can be shown to be:

$$(2n-3)!! = \prod_{i=2}^{n}(2i - 3)$$ (9.1)

which is of course super-exponential - for n=20, for instance, there are about 10²¹ such trees. This means that exhaustive enumeration is unfeasible even for a relatively small number of species. The next sections will present several approaches towards defining a target function, and attempting to solve the problem for that target function.