Matching Free Trees with Replicator Equations

Motivated by our recent work on rooted tree matching, in this paper we provide a solution to the problem of matching two free (i.e., unrooted) trees by constructing an association graph whose maximal cliques are in one-to-one correspondence with maximal common subtrees. We then solve the problem using simple replicator dynamics from evolutionary game theory. Experiments on hundreds of uniformly random trees are presented. The results are impressive: despite the inherent inability of these simple dynamics to escape from local optima, they always returned a globally optimal solution.