A Polynomial-Time Metric for Attributed Trees

Abstract

We address the problem of comparing attributed trees and propose a novel distance measure centered around the notion of a maximal similarity common subtree. The proposed measure is general and defined on trees endowed with either symbolic or continuous-valued attributes, and can be equally applied to ordered and unordered, rooted and unrooted trees. We prove that our measure satisfies the metric constraints and provide a polynomial-time algorithm to compute it. This is a remarkable and attractive property since the computation of traditional edit-distance-based metrics is NP-complete, except for ordered structures. We experimentally validate the usefulness of our metric on shape matching tasks, and compare it with edit-distance measures.

Learning shape-classes using a mixture of tree-unions

“…We compare the clusters obtained with the mixture of tree-unions approach with the result obtained by applying the pairwise clustering algorithm to two different distance measure. The first of these is approximate edit-distance described in [37], while the second is a tree distance metric that can be computed in polynomial time [38]. The distance metric between trees t 1 and t 2 is computed using the function ðu; vÞ that gauges the similarity between node u in t 1 and node v in t 2 .…”

Modeling and implementing software architecture with acme and archJava

“…We then detect structural differences ( Figure 2) between subsets of the two intermediate representations using our implementation of a tree-to-tree correction algorithm for unordered labeled trees based on [3]. The selection of the subset is under user control: if the Acme model does not specify some information that exists in ArchJava (such as method signatures), this information can be excluded from the comparison to avoid false positives.…”