The task of the quartet puzzling problem is to find a best-fitting binary X-tree for a finite n-set
from confidence values for the 3n4 binary trees with exactly four leaves from X, its fitness
being measured by the sum of the confidence values of all “induced” four-leaves subtrees.
We describe a method for finding an exact solution of this problem by integer linear
programming. Similar procedures can also be used for finding, eg best-fitting “circular”
networks. A crucial problem in this context is, of course, how to obtain the input confidence …