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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.
SHARC: Fast and robust unidirectional routing
 IN: WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS (ALENEX
, 2008
"... During the last years, impressive speedup techniques for Dijkstra’s algorithm have been developed. Unfortunately, the most advanced techniques use bidirectional search which makes it hard to use them in scenarios where a backward search is prohibited. Even worse, such scenarios are widely spread, e ..."
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Cited by 52 (20 self)
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During the last years, impressive speedup techniques for Dijkstra’s algorithm have been developed. Unfortunately, the most advanced techniques use bidirectional search which makes it hard to use them in scenarios where a backward search is prohibited. Even worse, such scenarios are widely spread, e.g., timetableinformation systems or timedependent networks. In this work, we present a unidirectional speedup technique which competes with bidirectional approaches. Moreover, we show how to exploit the advantage of unidirectional routing for fast exact queries in timetable information systems and for fast approximative queries in timedependent scenarios. By running experiments on several inputs other than road networks, we show that our approach is very robust to the input.
TimeDependent Route Planning
 Robust and Online LargeScale Optimization, LNCS
, 2009
"... Abstract. In this paper, we present an overview over existing speedup techniques for timedependent route planning. Apart from only explaining each technique one by one, we follow a more systematic approach. We identify basic ingredients of these recent techniques and show how they need to be augmen ..."
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Cited by 44 (17 self)
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Abstract. In this paper, we present an overview over existing speedup techniques for timedependent route planning. Apart from only explaining each technique one by one, we follow a more systematic approach. We identify basic ingredients of these recent techniques and show how they need to be augmented to guarantee correctness in timedependent networks. With the ingredients adapted, three efficient speedup techniques can be set up: CoreALT, SHARC, and Contraction Hierarchies. Experiments on realworld data deriving from road networks and public transportation confirm that these techniques allow the fast computation of timedependent shortest paths. 1
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
Distributed TimeDependent Contraction Hierarchies
 In Proceedings of the 9th International Symposium on Experimental Algorithms, volume 6049 of LNCS
, 2010
"... Abstract. Server based route planning in road networks is now powerful enough to find quickest paths in a matter of milliseconds, even if detailed information on timedependent travel times is taken into account. However this requires huge amounts of memory on each query server and hours of preproce ..."
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Cited by 12 (7 self)
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Abstract. Server based route planning in road networks is now powerful enough to find quickest paths in a matter of milliseconds, even if detailed information on timedependent travel times is taken into account. However this requires huge amounts of memory on each query server and hours of preprocessing even for a medium sized country like Germany. This is a problem since global internet companies would like to work with transcontinental networks, detailed models of intersections, and regular repreprocessing that takes the current traffic situation into account. By giving a distributed memory parallelization of the arguably best current technique – timedependent contraction hierarchies, we remove these bottlenecks. For example, on a medium size network 64 processes accelerate preprocessing by a factor of 28 to 160 seconds, reduce per process memory consumption by a factor of 10.5 and increase query throughput by a factor of 25. Key words: timedependent shortest paths, distributed computation, message passing, algorithm engineering 1
Optimal Route Planning for Electric Vehicles in Large Network
 In Burgard and Roth [5
"... We consider the problem of routing electric vehicles (EV) in the most energyefficient way within a road network taking into account both their limited energy supply as well as their ability to recuperate energy. Employing a classical result by Johnson and an observation about Dijkstra under nonc ..."
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Cited by 12 (0 self)
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We consider the problem of routing electric vehicles (EV) in the most energyefficient way within a road network taking into account both their limited energy supply as well as their ability to recuperate energy. Employing a classical result by Johnson and an observation about Dijkstra under nonconstant edge costs we obtainO(n log n+m) query time after aO(nm) preprocessing phase for any road network graph whose edge costs represent energy consumption or recuperation. If the energy recuperation is height induced in a very natural way, the preprocessing phase can even be omitted. We then adapt a technique for speedingup (unconstrained) shortest path queries to our scenario to achieve a speedup of another factor of around 20. Our results drastically improve upon the recent results in (Artmeier et al. 2010) and allow for route planning of EVs in an instant even on large networks.
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.
Bidirectional A ∗ Search on TimeDependent Road Networks
, 2010
"... The computation of pointtopoint shortest paths on timedependent road networks has a large practical interest, but very few works propose efficient algorithms for this problem. We propose a novel approach which tackles one of the main complications of route planning in timedependent graphs, which ..."
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Cited by 6 (1 self)
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The computation of pointtopoint shortest paths on timedependent road networks has a large practical interest, but very few works propose efficient algorithms for this problem. We propose a novel approach which tackles one of the main complications of route planning in timedependent graphs, which is the difficulty of using bidirectional search: since the exact arrival time at the destination is unknown, we start a backward search from the destination node using lower bounds on arc costs in order to restrict the set of nodes that have to be explored by the forward search. Our algorithm is based on A ∗ with landmarks (ALT); extensive computational results show that it is very effective in practice if we are willing to accept a small approximation factor, resulting in a speedup of more than one order of magnitude with respect to Dijkstra’s algorithm while finding only slightly suboptimal solutions. The main idea presented here can also be generalized to other types of search algorithms.
Parallel TimeDependent Contraction Hierarchies
 Master’s thesis, Universität Karlsruhe (TH), Fakultät für Informatik
, 2009
"... TimeDependent Contraction Hierarchies is a routing technique that solves the shortest path problem in graphs with timedependent edge weights, that have to satisfy the FIFO property. Although it shows great speedups over Dijkstra’s Algorithm the preprocessing is slow. We present a parallelized vers ..."
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Cited by 6 (2 self)
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TimeDependent Contraction Hierarchies is a routing technique that solves the shortest path problem in graphs with timedependent edge weights, that have to satisfy the FIFO property. Although it shows great speedups over Dijkstra’s Algorithm the preprocessing is slow. We present a parallelized version of the preprocessing taking advantage of the multiple cores present in todays CPUs. Nodes independent of one another are found and processed in parallel. We give experimental results for the German road network. With 4 and 8 cores a speedup of up to 3.4 and 5.3 is achieved respectively. 1
Algorithms for Matching and Predicting Trajectories
"... We consider the following two problems: Map Matching: Given a sequence of (imprecise) location measurements from a mobile user moving on a road network, determine the most likely path in the network this user has travelled along. Prediction of Trajectories: Given the path of where a mobile user has ..."
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Cited by 5 (1 self)
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We consider the following two problems: Map Matching: Given a sequence of (imprecise) location measurements from a mobile user moving on a road network, determine the most likely path in the network this user has travelled along. Prediction of Trajectories: Given the path of where a mobile user has moved along in a road network up to now, predict where he will travel along in the near future. Our map matching algorithm is simple and efficient even in case of very imprecise measurements like GSMlocalizations and allows for the realtime tracking of a large number of mobile users on modest hardware. Our proposed path prediction algorithm is equally simple but yields extremely accurate predictions at a very low computational cost. 1