Polynomial-time metrics for attributed trees
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Updated: Aug 17, 2026

Tree Core Analysis with X-ray Computed Tomography
Published on: September 22, 2023
Andrea Torsello1, Dzena Hidović-Rowe, Marcello Pelillo
1Dipartimento di Informatica, Università Ca' Foscari di Venezia, Via Torino 155, 30172 Venezia Mestre, Italy. torsello@dsi.unive.it
Abstract:
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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