On Nearest Neighbor Indexing of Nonlinear Trajectories

Abstract

In recent years, the problem of indexing mobile objects has assumed great importance because of its relevance to a wide variety of applications. Most previous results in this area have proposed indexing schemes for objects with linear trajectories in one or two dimensions. In this paper, we present methods for indexing objects with nonlinear trajectories. Specifically, we identify a useful condition called the convex hull property and show that any trajectory satisfying this condition can be indexed by storing a careful representation of these objects in a traditional index structure. Since a wide variety of relevant nonlinear trajectories satisfy this condition, our result significantly expands the class of trajectories for which nearest neighbor indexing schemes can be devised. We also show that even though many non-linear trajectories do not satisfy the convex hull condition, an approximate representation can often be found which satisfies it. We discuss examples of techniques which can be utilized to find representations that satisfy the convex hull property. We present empirical results to demonstrate the effectiveness of our indexing method.