TRGST: An enhanced generalized suffix tree for topological relations between paths

This paper introduces the TRGST data structure, which is designed to handle queries related to topological relations between paths represented as sequences of stops in a network. As an example, these paths could correspond to stops on a public transport network, and a query of interest is to retrieve paths that share at least $k$ consecutive stops. While topological relations among spatial objects have received extensive attention, the efficient processing of these relations in the context of trajectory paths, considering both time and space efficiency, remains a relatively less explored domain. Taking inspiration from pattern matching implementations, the TRGST data structure is constructed on the foundation of the Generalized Suffix Tree. Its purpose is to provide a compact representation of a set of paths and to efficiently handle topological relation queries by leveraging the pattern search capabilities inherent in this structure. The paper provides a detailed account of the structure and algorithms of TRGST, followed by a performance analysis utilizing both real and synthetic data. The results underscore the remarkable scalability of the TRGST in terms of both query time and space utilization.