In this paper, we describe an efficient indexing method for a shape-based similarity search of the trajectory of dynamically changing locations of people and mobile objects. In order to manage trajectories in database systems, we define a data model of trajectories as directed lines in a space, and the similarity between trajectories is defined as the Euclidean distance between directed discret...

This paper presents methods using algebraic topology for showing that pseudo-trajectories are close to trajectories of a dynamical system. Our emphasis is the case where the trajectories are unstable in two or more dimensions. We develop the algebraic topology for guaranteeing the existence of such trajectories.