Time-Dependent Contraction Hierarchies. (2009)

by Gernot Veit Batz, Daniel Delling, Peter Sanders, Christian Vetter
Venue:In Proceedings of the 11th Workshop on Algorithm Engineering and Experiments (ALENEX’09),
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Combining Hierarchical and Goal-Directed Speed-Up Techniques for Dijkstra’s Algorithm

by Reinhard Bauer, Daniel Delling, Peter Sanders, Dennis Schieferdecker, Dominik Schultes, Dorothea Wagner - 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 goal-directed 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 ..."
Abstract - Cited by 60 (24 self) - Add to MetaCart
In recent years, highly effective hierarchical and goal-directed 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 time-expanded timetables. Besides these quantitative results, we obtain general insights for successful combinations.
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SHARC: Fast and robust unidirectional routing

by Reinhard Bauer, Daniel Delling - IN: WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS (ALENEX , 2008
"... During the last years, impressive speed-up 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 ..."
Abstract - Cited by 52 (20 self) - Add to MetaCart
During the last years, impressive speed-up 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., timetable-information systems or timedependent networks. In this work, we present a unidirectional speed-up 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 time-dependent scenarios. By running experiments on several inputs other than road networks, we show that our approach is very robust to the input.

Time-Dependent Route Planning

by Daniel Delling, Dorothea Wagner - Robust and Online Large-Scale Optimization, LNCS , 2009
"... Abstract. In this paper, we present an overview over existing speed-up 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 ..."
Abstract - Cited by 44 (17 self) - Add to MetaCart
Abstract. In this paper, we present an overview over existing speed-up 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 time-dependent networks. With the ingredients adapted, three efficient speed-up techniques can be set up: Core-ALT, SHARC, and Contraction Hierarchies. Experiments on real-world data deriving from road networks and public transportation confirm that these techniques allow the fast computation of time-dependent shortest paths. 1
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Time-Dependent SHARC-Routing

by Daniel Delling - In Proceedings of the 16th Annual European Symposium on Algorithms (ESA’08 , 2008
"... In recent years, many speed-up 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 time-dependent networks which, unfortunately, appear quite frequently in ..."
Abstract - Cited by 17 (9 self) - Add to MetaCart
In recent years, many speed-up 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 time-dependent networks which, unfortunately, appear quite frequently in reality: Roads are predictably congested by traffic jams, and efficient timetable information systems rely on time-dependent networks. Hence, a fast technique for routing in such networks is needed. In this work, we present an efficient time-dependent 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 time-dependent scenario. As a result, we are able to efficiently compute exact shortest paths in time-dependent continental-sized transporta-tion networks, both of roads and of railways. It should be noted that time-dependent SHARC was the first efficient algorithm for time-dependent route planning. 1
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Distributed Time-Dependent Contraction Hierarchies

by Tim Kieritz, Dennis Luxen, Peter S, Christian Vetter - 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 time-dependent 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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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 time-dependent 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 re-preprocessing that takes the current traffic situation into account. By giving a distributed memory parallelization of the arguably best current technique – time-dependent 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: time-dependent shortest paths, distributed computation, message passing, algorithm en-gineering 1
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Optimal Route Planning for Electric Vehicles in Large Network

by Jochen Eisner, Stefan Funke, Sabine Stor - In Burgard and Roth [5
"... We consider the problem of routing electric vehicles (EV) in the most energy-efficient way within a road network tak-ing into account both their limited energy supply as well as their ability to recuperate energy. Employing a classical re-sult by Johnson and an observation about Dijkstra under non-c ..."
Abstract - Cited by 12 (0 self) - Add to MetaCart
We consider the problem of routing electric vehicles (EV) in the most energy-efficient way within a road network tak-ing into account both their limited energy supply as well as their ability to recuperate energy. Employing a classical re-sult by Johnson and an observation about Dijkstra under non-constant edge costs we obtainO(n log n+m) query time af-ter aO(nm) preprocessing phase for any road network graph whose edge costs represent energy consumption or recuper-ation. 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 speeding-up (unconstrained) shortest path queries to our scenario to achieve a speed-up 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.
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Online Computation of Fastest Path in Time-Dependent Spatial Networks

by Ugur Demiryurek, Farnoush Banaei-kashani, Cyrus Shahabi, et al. , 2011
"... The problem of point-to-point fastest path computation in static spatial networks is extensively studied with many precomputation techniques proposed to speed-up the computation. Most of the existing approaches make the simplifying assumption that travel-times of the network edges are constant. Howe ..."
Abstract - Cited by 8 (5 self) - Add to MetaCart
The problem of point-to-point fastest path computation in static spatial networks is extensively studied with many precomputation techniques proposed to speed-up the computation. Most of the existing approaches make the simplifying assumption that travel-times of the network edges are constant. However, with real-world spatial networks the edge travel-times are time-dependent, where the arrival-time to an edge determines the actual travel-time on the edge. In this paper, we study the online computation of fastest path in time-dependent spatial networks and present a technique which speeds-up the path computation. We show that our fastest path computation based on a bidirectional time-dependent A * search significantly improves the computation time and storage complexity. With extensive experiments using real data-sets (including a variety of large spatial networks with real traffic data) we demonstrate the efficacy of our proposed techniques for online fastest path computation.
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Bidirectional A ∗ Search on Time-Dependent Road Networks

by Giacomo Nannicini, Daniel Delling, Dominik Schultes , 2010
"... The computation of point-to-point shortest paths on time-dependent 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 time-dependent graphs, which ..."
Abstract - Cited by 6 (1 self) - Add to MetaCart
The computation of point-to-point shortest paths on time-dependent 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 time-dependent 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 speed-up 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.
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Parallel Time-Dependent Contraction Hierarchies

by Christian Vetter, Supervised G. V. Batz - Master’s thesis, Universität Karlsruhe (TH), Fakultät für Informatik , 2009
"... Time-Dependent Contraction Hierarchies is a routing technique that solves the shortest path problem in graphs with time-dependent 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 ..."
Abstract - Cited by 6 (2 self) - Add to MetaCart
Time-Dependent Contraction Hierarchies is a routing technique that solves the shortest path problem in graphs with time-dependent 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 in-dependent 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
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Algorithms for Matching and Predicting Trajectories

by Jochen Eisner, Stefan Funke, Andre Herbst, Andreas Spillner, Sabine Stor
"... 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 ..."
Abstract - Cited by 5 (1 self) - Add to MetaCart
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 real-time 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
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