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Geometric SpeedUp Techniques for Finding Shortest Paths in Large Sparse Graphs
, 2003
"... In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. ..."
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Cited by 56 (14 self)
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In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We assume that a layout of the graph is given. From this layout, in the preprocessing, we determine for each edge a geometric object containing all nodes that can be reached on a shortest path starting with that edge. Based on these geometric objects, the search space for online computation can be reduced significantly. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are traffic networks, the typical field of application for this scenario.
Timetable Information: Models and Algorithms
, 2006
"... We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transfor ..."
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Cited by 9 (7 self)
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We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transform the problems into shortest path problems are reviewed, including issues like the modeling of realistic details (e.g., train transfers) and further optimization criteria (e.g., the number of transfers). An important topic is also multicriteria optimization, where in general all attractive connections with respect to several criteria shall be determined. Finally, we discuss the performance of the described algorithms, which is crucial for their application in a real system.
Dynamic Shortest Paths Containers
, 2004
"... Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G =(V,E), we store, for each edge (u, v) ∈ E, the bounding box of all nodes t ∈ V for which a shortest utpath sta ..."
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Cited by 9 (3 self)
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Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G =(V,E), we store, for each edge (u, v) ∈ E, the bounding box of all nodes t ∈ V for which a shortest utpath starts with (u, v). Shortest path queries can then be answered by Dijkstra’s algorithm restricted to edges where the corresponding bounding box contains the target. In this paper, we present new algorithms as well as an empirical study for the dynamic case of this problem, where edge weights are subject to change and the bounding boxes have to be updated. We evaluate the quality and the time for different update strategies that guarantee correct shortest paths in an interesting application to railway information systems, using realworld data from six European countries.
Generating node coordinates for shortestpath computations in transportation networks
 ACM Journal on Experimental Algorithmics
"... Speedup techniques that exploit given node coordinates have proven useful for shortestpath computations in transportation networks and geographic information systems. To facilitate the use of such techniques when coordinates are missing from some, or even all, of the nodes in a network we generate ..."
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Cited by 2 (0 self)
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Speedup techniques that exploit given node coordinates have proven useful for shortestpath computations in transportation networks and geographic information systems. To facilitate the use of such techniques when coordinates are missing from some, or even all, of the nodes in a network we generate artificial coordinates using methods from graph drawing. Experiments on a large set of German train timetables indicate that the speedup achieved with coordinates from our drawings is close to that achieved with the true coordinates—and in some special cases even better.
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 Proceedings of TACAS’98
, 1998
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Travel Planning With SelfMade Maps
, 2001
"... Speedup techniques that exploit given node coordinates have proven useful for shortestpath computations in transportation networks and geographic information systems. To facilitate the use of such techniques when coordinates are missing from some, or even all, of the nodes in a network we gene ..."
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Cited by 2 (1 self)
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Speedup techniques that exploit given node coordinates have proven useful for shortestpath computations in transportation networks and geographic information systems. To facilitate the use of such techniques when coordinates are missing from some, or even all, of the nodes in a network we generate artificial coordinates using methods from graph drawing. Experiments on a large set of German train timetables indicate that the speedup achieved with coordinates from our network drawings is close to that achieved with the actual coordinates.
Train Driver Scheduling
, 1999
"... The candidate confirms that the work submitted is her own and that appropriate credit has been given where reference has been made to the work of others. Acknowledgements I would like to thank my supervisor, Professor A. Wren for his help, guidance and encouragement. Most importantly, he gave me the ..."
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The candidate confirms that the work submitted is her own and that appropriate credit has been given where reference has been made to the work of others. Acknowledgements I would like to thank my supervisor, Professor A. Wren for his help, guidance and encouragement. Most importantly, he gave me the opportunity to get restarted on scheduling. I would like to thank Margaret Parker for her help and support throughout these years. I would also like to thank the scheduling staff of GNER, Thameslink, Northern Spirit and WAGN for providing us with the test data. Thanks are to the Engineering and Physical Sciences Research Council for providing the research grants. Finally, my thanks go to Raymond for his support and patience. ii This thesis describes research into solving the U.K. train driver scheduling problems, which are very complex compared to the bus or other public transport driver scheduling problems. A set covering approach comprising a shift generation stage followed by a