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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. We as ..."
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Cited by 53 (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.
Using Multilevel Graphs for Timetable Information in Railway Systems
 IN PROCEEDINGS 4TH WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS (ALENEX 2002), VOLUME 2409 OF SPRINGER LNCS
, 2002
"... In many fields of application shortest path finding problems in very large graphs arise. Scenarios where large numbers ofonW##O queries for shortest paths have to be processedin realtime appear for examplein tra#cinc5###HF5 systems.In such systems, the techn5Ww# con sidered to speed up the shortes ..."
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Cited by 26 (12 self)
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In many fields of application shortest path finding problems in very large graphs arise. Scenarios where large numbers ofonW##O queries for shortest paths have to be processedin realtime appear for examplein tra#cinc5###HF5 systems.In such systems, the techn5Ww# con sidered to speed up the shortest pathcomputation are usually basedon precomputed incomputed5 On approach proposedoften in thiscon text is a spacereduction where precomputed shortest paths are replaced by sin## edges with weight equal to thelenOq of the corresponres shortest path.In this paper, we give a first systematic experimen tal study of such a spacereduction approach. Wein troduce theconOkW of multilevel graph decomposition Foron specificapplication scenica from the field of timetable information in public tranc ort, we perform a detailed anai ysisan experimen tal evaluation of shortest path computation based on multilevel graph decomposition.
Efficient Models for Timetable Information in Public Transportation Systems
 ACM JOURNAL OF EXPERIMENTAL ALGORITHMICS
, 2008
"... We consider two approaches that model timetable information in public transportation systems as shortestpath problems in weighted graphs. In the timeexpanded approach, every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the timedependent approach t ..."
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Cited by 24 (10 self)
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We consider two approaches that model timetable information in public transportation systems as shortestpath problems in weighted graphs. In the timeexpanded approach, every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the timedependent approach the graph contains only one node per station. Both approaches have been recently considered for (a simplified version of) the earliest arrival problem, but little is known about their relative performance. Thus far, there are only theoretical arguments in favor of the timedependent approach. In this paper, we provide the first extensive experimental comparison of the two approaches. Using several realworld data sets, we evaluate the performance of the basic models and of several new extensions towards realistic modeling. Furthermore, new insights on solving bicriteria optimization problems in both models are presented. The timeexpanded approach turns out to be more robust for modeling more complex scenarios, whereas the timedependent approach shows a clearly better performance.
SpeedUp Techniques for ShortestPath Computations
 IN PROCEEDINGS OF THE 24TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS’07
, 2007
"... During the last years, several speedup techniques for Dijkstra’s algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They are usually based on a preprocessing that annotates the graph with additional information which can ..."
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Cited by 13 (7 self)
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During the last years, several speedup techniques for Dijkstra’s algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They are usually based on a preprocessing that annotates the graph with additional information which can be used to prune or guide the search. Timetable information in public transport is a traditional application domain for such techniques. In this paper, we provide a condensed overview of new developments and extensions of classic results. Furthermore, we discuss how combinations of speedup techniques can be realized to take advantage from different strategies.
Stochastic Local Search Algorithms for Multiobjective Combinatorial Optimization: Methods and Analysis
, 2006
"... ..."
Dynamic Shortest Paths Containers
, 2003
"... 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 ..."
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Cited by 7 (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
The smoothed number of Pareto optimal solutions in bicriteria integer optimization
 In Proc. of the 12th Int. Conf. on Integer Programming and Combinatorial Optimization (IPCO
, 2007
"... 1 Introduction We study integer optimization problems having two criteria, say profit andweight, which are to be optimized simultaneously. A common approach for solving such problems is generating the set of Pareto optimal solutions, also knownas the Pareto set. Pareto optimal solutions are optimal ..."
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Cited by 6 (4 self)
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1 Introduction We study integer optimization problems having two criteria, say profit andweight, which are to be optimized simultaneously. A common approach for solving such problems is generating the set of Pareto optimal solutions, also knownas the Pareto set. Pareto optimal solutions are optimal compromises of the two criteria in the sense that any improvement of one criterion implies an impairment to the other. In other words, a solution
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 5 (4 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.
Pareto Paths with SHARC
 Proceedings of the 8th International Symposium on Experimental Algorithms (SEA’09), volume 5526 of LNCS
, 2009
"... Abstract. Up to now, research on speedup techniques for DIJKSTRA’s algorithm focused on singlecriteria scenarios. The goal was to find the quickest route within a transportation network. However, the quickest route is often not the best one. A user might be willing to accept slightly longer travel ..."
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Cited by 5 (2 self)
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Abstract. Up to now, research on speedup techniques for DIJKSTRA’s algorithm focused on singlecriteria scenarios. The goal was to find the quickest route within a transportation network. However, the quickest route is often not the best one. A user might be willing to accept slightly longer travel times if the cost of the journey is less. A common approach to cope with such a situation is to find Paretooptimal (concerning other metrics than travel times) routes. Such routes have the property that each route is better than any other route with respect to at least one metric under consideration, e.g., travel costs or number of train changes. In this work, we study multicriteria search in road networks. On the one hand, we focus on the problem of limiting the number of Pareto paths. On the other hand, we present a multicriteria variant of our recent SHARC algorithm. 1