The optimal sequenced route query

Abstract

Real-world road-planning applications often result in the formulation of new variations of the nearest neighbor (NN) problem requiring new solutions. In this paper, we study an unexplored form of NN queries named optimal sequenced route (OSR) query in both vector and metric spaces. OSR strives to find a route of minimum length starting from a given source location and passing through a number of typed locations in a particular order imposed on the types of the locations. We first transform the OSR problem into a shortest path problem on a large planar graph. We show that a classic shortest path algorithm such as Dijkstra’s is impractical for most real-world scenarios. Therefore, we propose LORD, a light threshold-based iterative algorithm, which utilizes various thresholds to prune the locations that cannot belong to the optimal route. Then we propose R-LORD, an extension of LORD which uses R-tree to examine the threshold values more efficiently. Finally, for applications that cannot tolerate the Euclidean distance as estimation and require exact distance measures in metric spaces (e.g., road networks) we propose PNE that progressively issues NN queries on different point types to construct the optimal route for the OSR query. Our extensive experiments on both real-world and synthetic datasets verify that our algorithms significantly outperform a disk-based variation of the Dijkstra approach in terms of processing time (up to two orders of magnitude) and required workspace (up to 90% reduction on average).