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Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics
November 2002 (vol. 24 no. 11)
pp. 1535-1541

Abstract—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 payoff-monotonic dynamics from evolutionary game theory. We illustrate the power of the approach by matching articulated and deformed shapes described by shape-axis trees. Experiments on hundreds of larger, uniformly random trees are also 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.

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Index Terms:
Graph matching, combinatorial optimization, quadratic programming, dynamical systems, evolutionary game theory, shape recognition.
Citation:
Marcello Pelillo, "Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 11, pp. 1535-1541, Nov. 2002, doi:10.1109/TPAMI.2002.1046176
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