Equations , Maximal Cliques , and Graph Isomorphism

We present a new energy-minimization framework for the graph isomorphism problem which is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear one-to-one correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the so-called \replicator" equations, a class of straightforward continuousand discretetime dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results which are competitive with those obtained using more elaborate meaneld annealing heuristics.