Dijkstra's algorithm on-line: an empirical case study from public railroad transport
Journal of Experimental Algorithmics (JEA)
Using Multi-level Graphs for Timetable Information in Railway Systems
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Engineering highway hierarchies
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
The Shortcut Problem --- Complexity and Approximation
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Speed-up techniques for shortest-path computations
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Engineering fast route planning algorithms
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
WEA'07 Proceedings of the 6th international conference on Experimental 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
The Shortcut Problem --- Complexity and Approximation
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Preprocessing speed-up techniques is hard
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Algorithm engineering for route planning: an update
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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During the last years, speed-up techniques for Dijkstra 's algorithm have been developed that make the computation of shortest paths a matter of microseconds even on huge road networks. The most sophisticated methods enhance the graph by inserting shortcuts , i.e. additional edges, that represent shortest paths in the graph. Until now, all existing shortcut-insertion strategies are heuristics and no theoretical results on the topic are known. In this work, we formalize the problem of adding shortcuts as a graph augmentation problem, study the algorithmic complexity of the problem, give approximation algorithms and show how to stochastically evaluate a given shortcut assignment on graphs that are too big to evaluate it exactly.