t-Spanners as a Data Structure for Metric Space Searching

Abstract

A t-spanner, a subgraph that approximates graph distances within a precision factor t, is a well known concept in graph theory. In this paper we use it in a novel way, namely as a data structure for searching metric spaces. The key idea is to consider the t-spanner as an approximation of the complete graph of distances among the objects, and use it as a compact device to simulate the large matrix of distances required by successful search algorithms like AESA [Vidal 1986]. The t-spanner provides a time-space tradeoff where full AESA is just one extreme. We show that the resulting algorithm is competitive against current approaches, e.g., 1.5 times the time cost of AESA using only 3.21% of its space requirement, in a metric space of strings; and 1.09 times the time cost of AESA using only 3.83 % of its space requirement, in a metric space of documents. We also show that t-spanners provide better space-time tradeoffs than classical alternatives such as pivot-based indexes. Furthermore, we show that the concept of t-spanners has potential for large improvements.

This work has been supported in part by the Millenium Nucleus Center for Web Research, Grant P01-029-F, Mideplan, Chile (1st and 2nd authors), CYTED VII.19 RIBIDI Project (all authors), and AT&T LA Chile (2nd author).