The pq -gram distance between ordered labeled trees

Abstract

When integrating data from autonomous sources, exact matches of data items that represent the same real-world object often fail due to a lack of common keys. Yet in many cases structural information is available and can be used to match such data. Typically the matching must be approximate since the representations in the sources differ.We propose pq-grams to approximately match hierarchical data from autonomous sources and define the pq-gram distance between ordered labeled trees as an effective and efficient approximation of the fanout weighted tree edit distance. We prove that the pq-gram distance is a lower bound of the fanout weighted tree edit distance and give a normalization of the pq-gram distance for which the triangle inequality holds. Experiments on synthetic and real-world data (residential addresses and XML) confirm the scalability of our approach and show the effectiveness of pq-grams. ACM Reference Format:Augsten, N., Böhlen, M., and Gamper, J. 2010. The pq-gram distance between ordered labeled trees.

REST service testing based on inferred XML schemas

“…Although our inferencer provides schemas which are well defined and tied to the input documents, it could be improved. For example, the algorithm calculates the distance between XML elements used to compute the elements belonging to a complex type may be replaced with new algorithms such as the pq-gram distance calculation [16]. Another way of evolution would be to study how to apply the same processing to responses in JSON or other formats.…”

Synthetising changes in XML documents as PULs

“…Each operation is given a user-defined fixed cost, except for the relabeling operation that employs a user-provided function that compares the values of two nodes. XyDiff [11] computes hash values for all the subtrees of the analyzed trees using DOMHASH 2 , an efficient hashing function specifically tailored for XML subtrees. XyDiff then searches for exact matches in a bottom-up traversal and eagerly tries to expand them looking for common ancestors for the two trees, relying on the node names.…”

“…Augsten et al [2] propose an estimation of the tree edit-distance for ordered trees based on pq-grams, subtrees of a fixed shape corresponding to the substrings (called q-grams) used for string similarity evaluation. pq-grams are composed by a stem made of p elements (bound by the parent-child relation) and a base of q consecutive siblings: the last element of the stem is named anchor node.…”

“…To estimate PUL edit-distance, we extend the pq-gram approximated similarity measure [2]. pq-grams are a generalization of string q-grams: they are subtrees of fixed size and shape, composed by a stem made of p elements (bound by the parent-child relation) and a base of q consecutive siblings: the last element of the stem is named anchor node and the element of the base are children of this node.…”

“…As an extension of the proof given in [2], the computation of the pql-grams distance between two trees is in O(n log n). The number of nodes in both the source and target window is limited to a constant number.…”