Introduction to Algorithms
IEEE Transactions on Knowledge and Data Engineering
An Efficient Path Computation Model for Hierarchically Structured Topographical Road Maps
IEEE Transactions on Knowledge and Data Engineering
Roads, codes, and spatiotemporal queries
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Computing the shortest path: A search meets graph theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
Scalable network distance browsing in spatial databases
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
Engineering Route Planning Algorithms
Algorithmics of Large and Complex Networks
Path oracles for spatial networks
Proceedings of the VLDB Endowment
ACM Transactions on Algorithms (TALG)
Contraction hierarchies: faster and simpler hierarchical routing in road networks
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Query Processing Using Distance Oracles for Spatial Networks
IEEE Transactions on Knowledge and Data Engineering
Highway dimension, shortest paths, and provably efficient algorithms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Graph indexing of road networks for shortest path queries with label restrictions
Proceedings of the VLDB Endowment
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Shortest path and distance queries on road networks: an experimental evaluation
Proceedings of the VLDB Endowment
Shortest path and distance queries on road networks: towards bridging theory and practice
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
Shortest path and distance queries on road networks: towards bridging theory and practice
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
Efficient single-source shortest path and distance queries on large graphs
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
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Given two locations s and t in a road network, a distance query returns the minimum network distance from s to t, while a shortest path query computes the actual route that achieves the minimum distance. These two types of queries find important applications in practice, and a plethora of solutions have been proposed in past few decades. The existing solutions, however, are optimized for either practical or asymptotic performance, but not both. In particular, the techniques with enhanced practical efficiency are mostly heuristic-based, and they offer unattractive worst-case guarantees in terms of space and time. On the other hand, the methods that are worst-case efficient often entail prohibitive preprocessing or space overheads, which render them inapplicable for the large road networks (with millions of nodes) commonly used in modern map applications. This paper presents Arterial Hierarchy (AH), an index structure that narrows the gap between theory and practice in answering shortest path and distance queries on road networks. On the theoretical side, we show that, under a realistic assumption, AH answers any distance query in Õ(log α) time, where α = dmax/dmin, and dmax (resp. dmin) is the largest (resp. smallest) L∞ distance between any two nodes in the road network. In addition, any shortest path query can be answered in Õ(k + log α) time, where k is the number of nodes on the shortest path. On the practical side, we experimentally evaluate AH on a large set of real road networks with up to twenty million nodes, and we demonstrate that (i) AH outperforms the state of the art in terms of query time, and (ii) its space and pre-computation overheads are moderate.