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Polynomial-Time Metrics for Attributed Trees
July 2005 (vol. 27 no. 7)
pp. 1087-1099
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.

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Index Terms:
Index Terms- Metrics, tree matching, polynomial-time algorithms, shape recognition.
Citation:
Andrea Torsello, D?ena Hidovic-Rowe, Marcello Pelillo, "Polynomial-Time Metrics for Attributed Trees," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 7, pp. 1087-1099, July 2005, doi:10.1109/TPAMI.2005.146
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