Distance Landmarks Revisited for Road Graphs
Computing shortest distances is one of the fundamental problems on graphs, and remains a {\em challenging} task today. {\em Distance} {\em landmarks} have been recently studied for shortest distance queries with an auxiliary data structure, referred to as {\em landmark} {\em covers}. This paper studies how to apply distance landmarks for fast {\em exact} shortest distance query answering on large road graphs. However, the {\em direct} application of distance landmarks is {\em impractical} due to the high space and time cost. To rectify this problem, we investigate novel techniques that can be seamlessly combined with distance landmarks. We first propose a notion of {\em hybrid landmark covers}, a revision of landmark covers. Second, we propose a notion of {\em agents}, each of which represents a small subgraph and holds good properties for fast distance query answering. We also show that agents can be computed in {\em linear time}. Third, we introduce graph partitions to deal with the remaining subgraph that cannot be captured by agents. Fourth, we develop a unified framework that seamlessly integrates our proposed techniques and existing optimization techniques, for fast shortest distance query answering. Finally, we experimentally verify that our techniques significantly improve the efficiency of shortest distance queries, using real-life road graphs.