  With the growing focus on semantic searches and interpretations, an
increasing number of standardized vocabularies and ontologies are being
designed and used to describe data. We investigate the querying of objects
described by a tree-structured ontology. Specifically, we consider the case of
finding the top-k best pairs of objects that have been annotated with terms
from such an ontology when the object descriptions are available only at
runtime. We consider three distance measures. The first one defines the object
distance as the minimum pairwise distance between the sets of terms describing
them, and the second one defines the distance as the average pairwise term
distance. The third and most useful distance measure, earth mover's distance,
finds the best way of matching the terms and computes the distance
corresponding to this best matching. We develop lower bounds that can be
aggregated progressively and utilize them to speed up the search for top-k
object pairs when the earth mover's distance is used. For the minimum pairwise
distance, we devise an algorithm that runs in O(D + Tk log k) time, where D is
the total information size and T is the total number of terms in the ontology.
We also develop a novel best-first search strategy for the average pairwise
distance that utilizes lower bounds generated in an ordered manner. Experiments
on real and synthetic datasets demonstrate the practicality and scalability of
our algorithms.
