Combining hierarchical and goal-directed speed-up techniques for dijkstra's algorithm

@article{Bauer2010CombiningHA,
  title={Combining hierarchical and goal-directed speed-up techniques for dijkstra's algorithm},
  author={Reinhard Bauer and Daniel Delling and Peter Sanders and Dennis Schieferdecker and Dominik Schultes and Dorothea Wagner},
  journal={ACM J. Exp. Algorithmics},
  year={2010},
  volume={15}
}
In recent years, highly effective hierarchical and goal-directed speed-up techniques for routing in large road networks have been developed. This article makes a systematic study of combinations of such techniques. These combinations turn out to give the best results in many scenarios, including graphs for unit disk graphs, grid networks, and time-expanded timetables. Besides these quantitative results, we obtain general insights for successful combinations. 

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References

SHOWING 1-10 OF 67 REFERENCES
Combining speed-up techniques for shortest-path computations
TLDR
This work considers all possible combinations of four known techniques for Dijkstra's algorithm, namely, goal-directed search, bidirectional search, multilevel approach, and shortest-path containers, and shows how these can be implemented.
Engineering Route Planning Algorithms
TLDR
An overview of the techniques enabling the development of algorithms for route planning in transportation networks and point out frontiers of ongoing research on more challenging variants of the problem that include dynamically changing networks, time-dependent routing, and flexible objective functions.
Highway Hierarchies Hasten Exact Shortest Path Queries
TLDR
A new speedup technique for route planning that exploits the hierarchy inherent in real world road networks and preprocesses the eight digit number of nodes needed for maps of the USA or Western Europe in a few hours using linear space.
14. Experimental Study on Speed-Up Techniques for Timetable Information Systems
TLDR
It turns out that recently developed techniques are much slower on graphs derived from timetable information than on road networks, and amazing insights are gained into the behavior of speed-up techniques in general.
Time-Dependent Contraction Hierarchies
TLDR
This is the first hierarchical speedup technique for time-dependent routing that allows bidirectional query algorithms and outperforms previous techniques with respect to query time using comparable or lower preprocessing time.
Time-Dependent SHARC-Routing
TLDR
This work presents an efficient time-dependent route planning algorithm based on the recently introduced SHARC algorithm, which is able to efficiently compute exact shortest paths in time- dependent continental-sized transportation networks, both of roads and of railways.
Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks
TLDR
CHs can be combined with many other route planning techniques, leading to improved performance for many-to-many routing, transit-node routing, goal-directed routing or mobile and dynamic scenarios, and a hierarchical query algorithm using bidirectional shortest-path search is obtained.
SHARC: Fast and robust unidirectional routing
TLDR
This work presents a unidirectional speed-up technique, which competes with bidirectional approaches, and shows how to exploit the advantage of uniddirectional routing for fast exact queries in timetable information systems and for fast approximative queries in time-dependent scenarios.
Better Landmarks Within Reach
TLDR
A practical algorithm for the point-to-point shortest path problem on road networks that combines A* search, landmark-based lower bounds, and reach-based pruning is presented, which makes preprocessing and queries faster while reducing the overall space requirements.
Landmark-Based Routing in Dynamic Graphs
TLDR
It turns out that by increasing the efficiency of ALT, one is able to perform fast (down to 20 ms on the Western European network) random queries in a dynamic scenario without updating the preprocessing as long as the changes in the network are moderate.
...
...