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Contraction hierarchies: Faster and simpler . . .
, 2008
"... We present a route planning technique solely based on the concept of node contraction. We contract or remove one node at a time out of the graph and add shortcut edges to the remaining graph to preserve shortest paths distances. The resulting contraction hierarchy (CH), the original graph plus short ..."
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Cited by 120 (34 self)
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We present a route planning technique solely based on the concept of node contraction. We contract or remove one node at a time out of the graph and add shortcut edges to the remaining graph to preserve shortest paths distances. The resulting contraction hierarchy (CH), the original graph plus shortcuts, also defines an order of “importance ” among all nodes through the node selection. We apply a modified bidirectional Dĳkstra algorithm that takes advantage of this node order to obtain shortest paths. The search space is reduced by relaxing only edges leading to more important nodes in the forward search and edges coming from more important nodes in the backward search. Both search scopes eventually meet at the most important node on a shortest path. We use a simple but extensible heuristic to obtain the node order: a priority queue whose priority function for each node is a linear combination of several terms, e.g. one term weights nodes depending on the sparsity of the remaining graph after the contraction. Another term regards the already contracted nodes to allow a more uniform contraction. Depending on the application we can select the combination of the priority terms to obtain the required hierarchy.
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 82 (39 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.
Engineering Highway Hierarchies
, 2006
"... Highway hierarchies exploit hierarchical properties inherent in realworld road networks to allow fast and exact pointtopoint shortestpath queries. A fast preprocessing routine iteratively performs two steps: first, it removes edges that only appear on shortest paths close to source or target; s ..."
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Cited by 69 (6 self)
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Highway hierarchies exploit hierarchical properties inherent in realworld road networks to allow fast and exact pointtopoint shortestpath queries. A fast preprocessing routine iteratively performs two steps: first, it removes edges that only appear on shortest paths close to source or target; second, it identifies lowdegree nodes and bypasses them by introducing shortcut edges. The resulting hierarchy of highway networks is then used in a Dijkstralike bidirectional query algorithm to considerably reduce the search space size without losing exactness. The crucial fact is that ‘far away ’ from source and target it is sufficient to consider only highlevel edges. Various experiments with realworld road networks confirm the performance of our approach. On a 2.0 GHz machine, preprocessing the network of Western Europe, which consists of about 18 million nodes, takes 13 minutes and yields 48 bytes of additional data per node. Then, random queries take 0.61 ms on average. If we are willing to accept slower query times (1.10 ms), the memory usage can be decreased to 17 bytes per node. We can guarantee that at most 0.014 % of all nodes are visited during any query. Results for US road networks are similar. Highway hierarchies can be combined with goaldirected search, they can be extended to answer manytomany queries, and they are a crucial ingredient for other speedup techniques, namely for transitnode routing and highwaynode routing.
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 60 (24 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 33 (4 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.
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 20 (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.
Mobile Route Planning
"... We provide an implementation of an exact route planning algorithm on a mobile device that answers shortestpath queries in a road network of a whole continent instantaneously, i.e., with a delay of about 100ms, which is virtually not observable for a human user. We exploit spatial and hierarchical ..."
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Cited by 19 (2 self)
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We provide an implementation of an exact route planning algorithm on a mobile device that answers shortestpath queries in a road network of a whole continent instantaneously, i.e., with a delay of about 100ms, which is virtually not observable for a human user. We exploit spatial and hierarchical locality properties to design a significantly compressed externalmemory graph representation, which can be traversed efficiently and which occupies only a few hundred megabytes for road networks with up to 34 million nodes. Next to the accuracy, the computational speed, and the low space requirements, the simplicity of our approach is a fourth argument that suggests an application of our implementation in car navigation systems.
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 18 (10 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.
TimeDependent SHARCRouting
 In Proceedings of the 16th Annual European Symposium on Algorithms (ESA’08
, 2008
"... In recent years, many speedup techniques for Dijkstra’s algorithm have been developed that make the computation of shortest paths in static road networks a matter of microseconds. However, only few of those techniques work in timedependent networks which, unfortunately, appear quite frequently in ..."
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Cited by 17 (9 self)
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In recent years, many speedup techniques for Dijkstra’s algorithm have been developed that make the computation of shortest paths in static road networks a matter of microseconds. However, only few of those techniques work in timedependent networks which, unfortunately, appear quite frequently in reality: Roads are predictably congested by traffic jams, and efficient timetable information systems rely on timedependent networks. Hence, a fast technique for routing in such networks is needed. In this work, we present an efficient timedependent route planning algorithm. It is based on our recently introduced SHARC algorithm, which we adapt by augmenting its basic ingredients such that correctness can still be guaranteed in a timedependent scenario. As a result, we are able to efficiently compute exact shortest paths in timedependent continentalsized transportation networks, both of roads and of railways. It should be noted that timedependent SHARC was the first efficient algorithm for timedependent route planning. 1
Route Planning with Flexible Objective Functions
 In Proceedings of the 12th Workshop on Algorithm Engineering and Experiments (ALENEX’10), 124–137. SIAM
"... Abstract We present the first fast route planning algorithm that answers shortest paths queries for a customizable linear combination of two different metrics, e. g. travel time and energy cost, on large scale road networks. The precomputation receives as input a directed graph, two edge weight fun ..."
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Cited by 10 (4 self)
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Abstract We present the first fast route planning algorithm that answers shortest paths queries for a customizable linear combination of two different metrics, e. g. travel time and energy cost, on large scale road networks. The precomputation receives as input a directed graph, two edge weight functions t(e) and c(e), and a discrete interval [L, U ]. The resulting flexible query algorithm finds for a parameter p ∈ [L, U ] an exact shortest path for the edge weight t(e)+p·c(e). This allows for different tradeoffs between the two edge weight functions at query time. We apply precomputation based on node contraction, which adds all necessary shortcuts for any parameter choice efficiently. To improve the node ordering, we developed the new concept of gradual parameter interval splitting. Additionally, we improve performance by combining node contraction and a goaldirected technique in our flexible scenario.