t-Spanners for metric space searching

• Authors: Gonzalo Navarro;Rodrigo Paredes;Edgar Chávez
• Venue: Data & Knowledge Engineering
• Year: 2007

The problem of Proximity Searching in Metric Spaces consists in finding the elements of a set which are close to a given query under some similarity criterion. In this paper we present a new methodology to solve this problem, which uses a t-spanner G'(V,E) as the representation of the metric database. A t-spanner is a subgraph G'(V,E) of a graph G(V,A), such that E@?A and G' approximates the shortest path costs over G within a precision factor t. Our key idea is to regard the t-spanner as an approximation to the complete graph of distances among the objects, and to use it as a compact device to simulate the large matrix of distances required by successful search algorithms such as AESA. The t-spanner properties imply that we can use shortest paths over G' to estimate any distance with bounded-error factor t. For this sake, several t-spanner construction, updating, and search algorithms are proposed and experimentally evaluated. We show that our technique is competitive against current approaches. For example, in a metric space of documents our search time is only 9% over AESA, yet we need just 4% of its space requirement. Similar results are obtained in other metric spaces. Finally, we conjecture that the essential metric space property to obtain good t-spanner performance is the existence of clusters of elements, and enough empirical evidence is given to support this claim. This property holds in most real-world metric spaces, so we expect that t-spanners will display good behavior in most practical applications. Furthermore, we show that t-spanners have a great potential for improvements.