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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.
Timedependent contraction hierarchies
 IN PROC. 11TH WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS (ALENEX
, 2009
"... Contraction hierarchies are a simple hierarchical routing technique that has proved extremely efficient for static road networks. We explain how to generalize them to networks with timedependent edge weights. This is the first hierarchical speedup technique for timedependent routing that allows bid ..."
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Cited by 23 (10 self)
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Contraction hierarchies are a simple hierarchical routing technique that has proved extremely efficient for static road networks. We explain how to generalize them to networks with timedependent edge weights. This is the first hierarchical speedup technique for timedependent routing that allows bidirectional query algorithms. For large realistic networks with considerable timedependence (Germany, weekdays) our method outperforms previous techniques with respect to query time using comparable or lower preprocessing time.
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
Online Computation of Fastest Path in TimeDependent Spatial Networks
, 2011
"... The problem of pointtopoint fastest path computation in static spatial networks is extensively studied with many precomputation techniques proposed to speedup the computation. Most of the existing approaches make the simplifying assumption that traveltimes of the network edges are constant. Howe ..."
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Cited by 8 (5 self)
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The problem of pointtopoint fastest path computation in static spatial networks is extensively studied with many precomputation techniques proposed to speedup the computation. Most of the existing approaches make the simplifying assumption that traveltimes of the network edges are constant. However, with realworld spatial networks the edge traveltimes are timedependent, where the arrivaltime to an edge determines the actual traveltime on the edge. In this paper, we study the online computation of fastest path in timedependent spatial networks and present a technique which speedsup the path computation. We show that our fastest path computation based on a bidirectional timedependent A * search significantly improves the computation time and storage complexity. With extensive experiments using real datasets (including a variety of large spatial networks with real traffic data) we demonstrate the efficacy of our proposed techniques for online fastest path computation.
On the Complexity of TimeDependent Shortest Paths
"... We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomialsize) piecewise line ..."
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Cited by 4 (0 self)
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We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomialsize) piecewise linear, the shortest path from s to d can change Θ(log n) n times, settling a severalyearold conjecture of Dean [Technical Reports, 1999, 2004]. We also show that the complexity is polynomial if the slopes of the linear function come from a restricted class, present an outputsensitive algorithm for the general case, and describe a scheme for a (1 + ɛ)approximation of the travel time function in nearquadratic space. Finally, despite the fact that the arrival time function may have superpolynomial complexity, we show that a minimum delay path for any departure time interval can be computed in polynomial time. 1
SpaceEfficient SHARCRouting
, 2009
"... Accelerating the computation of quickest paths in road networks has been undergoing a rapid development during the last years. The breakthrough idea for handling road networks with tens of millions of nodes was the concept of shortcuts, i.e., additional arcs that represent long paths in the input. V ..."
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Cited by 3 (1 self)
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Accelerating the computation of quickest paths in road networks has been undergoing a rapid development during the last years. The breakthrough idea for handling road networks with tens of millions of nodes was the concept of shortcuts, i.e., additional arcs that represent long paths in the input. Very recently, this concept has been transferred to timedependent road networks where travel times on arcs are given by functions. Unfortunately, the concept of shortcuts yields a high increase in space consumption for timedependent road networks since the travel time functions assigned to the shortcuts may become quite complex. In this work, we present how the space overhead induced by timedependent SHARC, a technique relying on shortcuts as well, can be reduced significantely. As a result, we are able to reduce the overhead stemming from SHARC by a factor of up to 11.5 for the price of a loss in query performance of a factor of 4. The methods we present allow a flexible tradeoff between space consumption and query performance.
Time dependent contraction hierarchies – basic algorithmic ideas
, 2008
"... Contraction hierarchies are a simple hierarchical routing technique that has proved extremely efficient for static road networks. We explain how to generalize them to networks with timedependent edge weights. This is the first hierarchical speedup technique for timedependent routing that allows bi ..."
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Cited by 3 (1 self)
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Contraction hierarchies are a simple hierarchical routing technique that has proved extremely efficient for static road networks. We explain how to generalize them to networks with timedependent edge weights. This is the first hierarchical speedup technique for timedependent routing that allows bidirectional query algorithms. 1
UniALT for Regular Language Constrained Shortest Paths on a MultiModal Transportation Network
 In Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS), A. Caprara
"... Shortest paths on road networks can be efficiently calculated using Dijkstra’s algorithm (D). In addition to roads, multimodal transportation networks include public transportation, bicycle lanes, etc. For paths on this type of network, further constraints, e.g., preferences in using certain modes ..."
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Cited by 2 (2 self)
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Shortest paths on road networks can be efficiently calculated using Dijkstra’s algorithm (D). In addition to roads, multimodal transportation networks include public transportation, bicycle lanes, etc. For paths on this type of network, further constraints, e.g., preferences in using certain modes of transportation, may arise. The regular language constrained shortest path problem deals with this kind of problem. It uses a regular language to model the constraints. The problem can be solved efficiently by using a generalization of Dijkstra’s algorithm (DRegLC). In this paper we propose an adaption of the speedup technique uniALT, in order to accelerate DRegLC. We call our algorithm SDALT. We provide experimental results on a realistic multimodal public transportation network including timedependent cost functions on arcs. The experiments show that our algorithm performs well, with speedups of a factor 2 to 20.