The algorithm design manual
Introduction to algorithms
Using Multi-level Graphs for Timetable Information in Railway Systems
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Dijkstra's Algorithm On-Line: An Empirical Case Study from Public Railroad Transport
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
Planar Graphs, Negative Weight Edges, Shortest Paths, and Near Linear Time
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Compact Oracles for Reachability and Approximate Distances in Planar Digraphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Computing the shortest path: A search meets graph theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Partitioning graphs to speedup Dijkstra's algorithm
Journal of Experimental Algorithmics (JEA)
Engineering highway hierarchies
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Engineering Route Planning Algorithms
Algorithmics of Large and Complex Networks
Fast paths in large-scale dynamic road networks
Computational Optimization and Applications
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Fast and compact oracles for approximate distances in planar graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Combining hierarchical and goal-directed speed-up techniques for Dijkstra's algorithm
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Contraction hierarchies: faster and simpler hierarchical routing in road networks
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Goal directed shortest path queries using precomputed cluster distances
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
Highway hierarchies hasten exact shortest path queries
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Acceleration of shortest path and constrained shortest path computation
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Partitioning graphs to speed up dijkstra's algorithm
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Heuristic techniques for accelerating hierarchical routing on road networks
IEEE Transactions on Intelligent Transportation Systems
Exact Routing in Large Road Networks Using Contraction Hierarchies
Transportation Science
Simple, fast, and scalable reachability oracle
Proceedings of the VLDB Endowment
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Highway hierarchies exploit hierarchical properties inherent in real-world road networks to allow fast and exact point-to-point shortest-path queries. A fast preprocessing routine iteratively performs two steps: First, it removes edges that only appear on shortest paths close to source or target; second, it identifies low-degree nodes and bypasses them by introducing shortcut edges. The resulting hierarchy of highway networks is then used in a Dijkstra-like bidirectional query algorithm to considerably reduce the search space size without losing exactness. The crucial fact is that ‘far away’ from source and target it is sufficient to consider only high-level edges. Experiments with road networks for a continent show that using a preprocessing time of around 15 min, one can achieve a query time of around 1ms on a 2.0GHz AMD Opteron. Highway hierarchies can be combined with goal-directed search, they can be extended to answer many-to-many queries, and they can be used as a basis for other speed-up techniques (e.g., for transit-node routing and highway-node routing).