Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation
Communications of the ACM
On finding and updating shortest paths distributively
Journal of Algorithms
Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length
Journal of the ACM (JACM)
Distributed computation on graphs: shortest path algorithms
Communications of the ACM
Dijkstra's Algorithm On-Line: An Empirical Case Study from Public Railroad Transport
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
Delta-Stepping: A Parallel Single Source Shortest Path Algorithm
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Efficient models for timetable information in public transportation systems
Journal of Experimental Algorithmics (JEA)
SHARC: Fast and robust unidirectional routing
Journal of Experimental Algorithmics (JEA)
Engineering Route Planning Algorithms
Algorithmics of Large and Complex Networks
Car or Public Transport--Two Worlds
Efficient Algorithms
Robust and Online Large-Scale Optimization: Models and Techniques for Transportation Systems
Robust and Online Large-Scale Optimization: Models and Techniques for Transportation Systems
Engineering Time-Expanded Graphs for Faster Timetable Information
Robust and Online Large-Scale Optimization
Robust and Online Large-Scale Optimization
Proceedings of the 7th international conference on Experimental algorithms
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
Multi-criteria shortest paths in time-dependent train networks
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Fast routing in very large public transportation networks using transfer patterns
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Finding all attractive train connections by multi-criteria Pareto search
ATMOS'04 Proceedings of the 4th international Dagstuhl, ATMOS conference on Algorithmic approaches for transportation modeling, optimization, and systems
Algorithmica - Special Issue: European Symposium on Algorithms
A hub-based labeling algorithm for shortest paths in road networks
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
Contraction of timetable networks with realistic transfers
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
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Exploiting parallelism in route planning algorithms is a challenging algorithmic problem with obvious applications in mobile navigation and timetable information systems. In this work, we present a novel algorithm for the one-to-all profile-search problem in public transportation networks. It answers the question for all fastest connections between a given station S and any other station at any time of the day in a single query. This algorithm allows for a very natural parallelization, yielding excellent speed-ups on standard multicore servers. Our approach exploits the facts that, first, time-dependent travel-time functions in such networks can be represented as a special class of piecewise linear functions and, second, only few connections from S are useful to travel far away. Introducing the connection-setting property, we are able to extend Dijkstra's algorithm in a sound manner. Furthermore, we also accelerate station-to-station queries by preprocessing important connections within the public transportation network. As a result, we are able to compute all relevant connections between two random stations in a complete public transportation network of a big city (New York) on a standard multi-core server in real time.