Stable Tree Labelling for Accelerating Distance Queries on Dynamic Road Networks

Abstract

Finding the shortest-path distance between two arbitrary vertices is an important problem in road networks. Due to real-time traffic conditions, road networks undergo dynamic changes all the time. Current state-of-the-art methods incrementally maintain a distance labelling based on a hierarchy among vertices to support efficient distance computation. However, their labelling sizes are often large and cannot be efficiently maintained. To combat these issues, we present a simple yet efficient labelling method, namely \emph{Stable Tree Labelling} (STL), for answering distance queries on dynamic road networks. We observe that the properties of an underlying hierarchy play an important role in improving and balancing query and update performance. Thus, we introduce the notion of \emph{stable tree hierarchy} which lays the ground for developing efficient maintenance algorithms on dynamic road networks. Based on stable tree hierarchy, STL can be efficiently constructed as a 2-hop labelling. A crucial ingredient of STL is to only store distances within subgraphs in labels, rather than distances in the entire graph, which restricts the labels affected by dynamic changes. We further develop two efficient maintenance algorithms upon STL: \emph{Label Search algorithm} and \emph{Pareto Search algorithm}. Label Search algorithm identifies affected ancestors in a stable tree hierarchy and performs efficient searches to update labels from those ancestors. Pareto Search algorithm explores the interaction between search spaces of different ancestors, and combines searches from multiple ancestors into only two searches for each update, eliminating duplicate graph traversals. The experiments show that our algorithms significantly outperform state-of-the-art dynamic methods in maintaining the labelling and query processing, while requiring an order of magnitude less space.