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24
Engineering Route Planning Algorithms
 ALGORITHMICS OF LARGE AND COMPLEX NETWORKS. LECTURE NOTES IN COMPUTER SCIENCE
, 2009
"... Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra’s algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on ..."
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Cited by 30 (18 self)
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Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra’s algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on more challenging variants of the problem that include dynamically changing networks, timedependent routing, and flexible objective functions.
Combining Hierarchical and GoalDirected SpeedUp Techniques for Dijkstra’s Algorithm
 PROCEEDINGS OF THE 7TH WORKSHOP ON EXPERIMENTAL ALGORITHMS (WEA’08), VOLUME 5038 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2008
"... In recent years, highly effective hierarchical and goaldirected speedup techniques for routing in large road networks have been developed. This paper makes a systematic study of combinations of such techniques. These combinations turn out to give the best results in many scenarios, including graphs ..."
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Cited by 27 (13 self)
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In recent years, highly effective hierarchical and goaldirected speedup techniques for routing in large road networks have been developed. This paper 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 timeexpanded timetables. Besides these quantitative results, we obtain general insights for successful combinations.
Engineering Fast Route Planning Algorithms
, 2007
"... Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to one million times faster than Dijkstra’s algorithm. We outline ideas, algorithms, implementations, and experimental methods behind this development. We also explai ..."
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Cited by 26 (3 self)
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Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to one million times faster than Dijkstra’s algorithm. We outline ideas, algorithms, implementations, and experimental methods behind this development. We also explain why the story is not over yet because dynamically changing networks, flexible objective functions, and new applications pose a lot of interesting challenges.
Combining SpeedUp Techniques for ShortestPath Computations
 In Proc. 3rd Workshop on Experimental and Efficient Algorithms. LNCS
, 2004
"... Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. ..."
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Cited by 23 (6 self)
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Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In most studies, such techniques are considered individually.
Highperformance multilevel graphs
 IN: 9TH DIMACS IMPLEMENTATION CHALLENGE
, 2006
"... Shortestpath computation is a frequent task in practice. Owing to evergrowing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortestpath algorithm have been devised. This work reviews the ..."
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Cited by 14 (4 self)
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Shortestpath computation is a frequent task in practice. Owing to evergrowing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortestpath algorithm have been devised. This work reviews the multilevel technique to answer shortestpath queries exactly [SWZ02, HSW06], which makes use of a hierarchical decomposition of the input graph and precomputation of supplementary information. We develop this preprocessing to the maximum and introduce several ideas to enhance this approach considerably, by reorganizing the precomputed data in partial graphs and optimizing them individually. To answer a given query, certain partial graphs are combined to a search graph, which can be explored by a simple and fast procedure. Experiments confirm query times of less than 200 µs for a road graph with over 15 million vertices.
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 14 (6 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.
Experimental Study on SpeedUp Techniques for Timetable Information Systems
 PROCEEDINGS OF THE 7TH WORKSHOP ON ALGORITHMIC APPROACHES FOR TRANSPORTATION MODELING, OPTIMIZATION, AND SYSTEMS (ATMOS 2007
, 2007
"... During the last years, impressive speedup techniques for DIJKSTRA’s algorithm have been developed. Unfortunately, recent research mainly focused on road networks. However, fast algorithms are also needed for other applications like timetable information systems. Even worse, the adaption of recentl ..."
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Cited by 11 (7 self)
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During the last years, impressive speedup techniques for DIJKSTRA’s algorithm have been developed. Unfortunately, recent research mainly focused on road networks. However, fast algorithms are also needed for other applications like timetable information systems. Even worse, the adaption of recently developed techniques to timetable information is more complicated than expected. In this work, we check whether results from road networks are transferable to timetable information. To this end, we present an extensive experimental study of the most prominent speedup techniques on different types of inputs. It turns out that recently developed techniques are much slower on graphs derived from timetable information than on road networks. In addition, we gain amazing insights into the behavior of speedup techniques in general.
Engineering the labelconstrained shortestpath algorithm
, 2007
"... Abstract. We consider a generalization of the shortestpath problem: given an alphabet Σ, a graph G whose edges are weighted and Σlabeled, and a regular language L ⊆ Σ∗, the Lconstrained shortestpath problem consists of finding a shortest path p in G such that the concatenated labels along p form ..."
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Cited by 10 (1 self)
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Abstract. We consider a generalization of the shortestpath problem: given an alphabet Σ, a graph G whose edges are weighted and Σlabeled, and a regular language L ⊆ Σ∗, the Lconstrained shortestpath problem consists of finding a shortest path p in G such that the concatenated labels along p form a word of L. This definition allows to model, e. g., many trafficplanning problems. We present extensions of wellknown speedup techniques for the standard shortestpath problem, and conduct an extensive experimental study of their performance with various networks and language constraints. Our results show that depending on the network type, both goaldirected and bidirectional search speed up the search considerably, while combinations of these do not. 1
Dynamic Multilevel Overlay Graphs for Shortest Paths
 Mathematics in Computer Science
, 2008
"... Multilevel overlay graphs represent a speedup technique for shortest paths computation which is based on a hierarchical decomposition of a weighted directed graph G. They have been shown to be experimentally efficient, especially when applied to timetable information. However, no theoretical resul ..."
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Cited by 5 (2 self)
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Multilevel overlay graphs represent a speedup technique for shortest paths computation which is based on a hierarchical decomposition of a weighted directed graph G. They have been shown to be experimentally efficient, especially when applied to timetable information. However, no theoretical result on the cost of constructing, maintaining and querying multilevel overlay graphs in a dynamic environment is known. In this paper, we show theoretical properties of multilevel overlay graphs that lead us to the definition of a new data structure for the computation and the maintenance of an overlay graph of G while weight decrease or weight increase operations are performed on G. Our solution is theoretically faster than the recomputation from scratch and allows queries that can be performed more efficiently than running Dijkstra’s shortest paths algorithm on G. 1
Graph Indexing of Road Networks for Shortest Path Queries with Label Restrictions
"... The current widespread use of locationbased services and GPS technologies has revived interest in very fast and scalable shortest path queries. We introduce a new shortest path query type in which dynamic constraints may be placed on the allowable set of edges that can appear on a valid shortest pa ..."
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Cited by 4 (0 self)
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The current widespread use of locationbased services and GPS technologies has revived interest in very fast and scalable shortest path queries. We introduce a new shortest path query type in which dynamic constraints may be placed on the allowable set of edges that can appear on a valid shortest path (e.g., dynamically restricting the type of roads or modes of travel which may be considered in a multimodal transportation network). We formalize this problem as a specific variant of formal language constrained shortest path problems, which we call the Kleene Language Constrained Shortest Paths problem. To efficiently support this type of dynamically constrained shortest path query for largescale datasets, we extend the hierarchical graph indexing technique known as Contraction Hierarchies. Our experimental evaluation using the North American road network dataset (with over 50 million edges) shows an average query speed and search space improvement of over 3 orders of magnitude compared to the naïve adaptation of the standard Dijkstra’s algorithm to support this query type. We also show an improvement of over 2 orders of magnitude compared to the only previouslyexisting indexing technique which could solve this problem without additional preprocessing. 1.