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Replicator Equations, Maximal Cliques, and Graph Isomorphism (1999)
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@MISC{Pelillo99replicatorequations,,
author = {Marcello Pelillo},
title = {Replicator Equations, Maximal Cliques, and Graph Isomorphism},
year = {1999}
}
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Abstract
We present a new energy-minimization framework for the graph isomorphism problem that 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 continuous- and discrete-time 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 that are competitive with those obtained using more elaborate mean-field annealing heuristics.
Keyphrases
graph isomorphism maximal clique replicator equation elaborate mean-field annealing heuristic clear one-to-one correspondence exists discrete-time dynamical system various branch maximum clique problem standard quadratic program combinatorial problem inherent inability graph isomorphism problem equivalent maximum clique formulation quadratic program so-called replicator equation new energy-minimization framework fundamental result attractive feature various way local solution theoretical biology experimental result
