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We address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree. The proposed measures are general and defined on trees endowed with either symbolic or continuous-valued attributes and can be applied to rooted as well as unrooted trees. We prove that our measures satisfy the metric constraints and provide a polynomial-time algorithm to compute them. This is a remarkable and attractive property, since the computation of traditional edit-distance-based metrics is, in general, NP-complete, at least in the unordered case. We experimentally validate the usefulness of our metrics on shape matching tasks and compare them with (an approximation of) edit-distance.
Index Terms- Metrics, tree matching, polynomial-time algorithms, shape recognition.

M. Pelillo, D. Hidovic-Rowe and A. Torsello, "Polynomial-Time Metrics for Attributed Trees," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 27, no. , pp. 1087-1099, 2005.
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