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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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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
Efficient Route Planning in Flight Networks
, 2009
"... We present a set of three new timedependent models with increasing flexibility for realistic route planning in flight networks. By these means, we obtain small graph sizes while modeling airport procedures in a realistic way. With these graphs, we are able to efficiently compute a set of best con ..."
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We present a set of three new timedependent models with increasing flexibility for realistic route planning in flight networks. By these means, we obtain small graph sizes while modeling airport procedures in a realistic way. With these graphs, we are able to efficiently compute a set of best connections with multiple criteria over a full day. It even turns out that due to the very limited graph sizes it is feasible to precompute full distance tables between all airports. As a result, best connections can be retrieved in a few microseconds on real world data.
A case for timedependent shortest path computation in spatial networks
 IN: PROC. OF THE SIGSPATIAL INTL. CONF. ON ADVANCES IN GIS
, 2010
"... The problem of pointtopoint shortest path computation in spatial networks is extensively studied with many approaches proposed to speedup the computation. Most of the existing approaches make the simplifying assumption that weights (e.g., traveltime) of the network edges are constant. However, w ..."
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The problem of pointtopoint shortest path computation in spatial networks is extensively studied with many approaches proposed to speedup the computation. Most of the existing approaches make the simplifying assumption that weights (e.g., traveltime) 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 of the edge. With this paper, we study the applicability of existing shortest path algorithms to realworld large timedependent spatial networks. In addition, we evaluate the importance of considering timedependent edge traveltimes for route planning in spatial networks. We show that timedependent shortest path computation can reduce the traveltime by 36 % on average as compared to the static shortest path computation that assumes constant edge traveltimes.
Core Routing on Dynamic TimeDependent Road Networks
, 2010
"... Route planning in large scale timedependent road networks is an important practical application of the shortest paths problem that greatly benefits from speedup techniques. In this paper we extend a twolevel hierarchical approach for pointtopoint shortest paths computations to the timedependent ..."
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Route planning in large scale timedependent road networks is an important practical application of the shortest paths problem that greatly benefits from speedup techniques. In this paper we extend a twolevel hierarchical approach for pointtopoint shortest paths computations to the timedependent case. This method, also known as core routing in the literature for static graphs, consists in the selection of a small subnetwork where most of the computations can be carried out, thus reducing the search space. We combine this approach with bidirectional goaldirected search in order to obtain an algorithm capable of finding shortest paths in a matter of milliseconds on continental sized networks. Moreover, we tackle the dynamic scenario where the piecewise linear functions that we use to model timedependent arc costs are not fixed, but can have their coefficients updated requiring only a small computational effort.
Distance Oracles for TimeDependent Networks
"... Abstract. We present the first approximate distance oracle for sparse directed networks with timedependent arctraveltimes determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes (1 + ε)−approximate distance summaries from selected la ..."
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Abstract. We present the first approximate distance oracle for sparse directed networks with timedependent arctraveltimes determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes (1 + ε)−approximate distance summaries from selected landmark vertices to all other vertices in the network, and provides two sublineartime query algorithms that deliver constant and (1+σ)−approximate shortesttraveltimes, respectively, for arbitrary origindestination pairs in the network. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about traveltime functions which allow the smooth transition towards asymmetric and timedependent distance metrics. 1
Pruning Techniques for the Stochastic ontime Arrival Problem An Experimental Study
"... Abstract. Computing shortest paths is one of the most researched topics in algorithm engineering. Currently available algorithms compute shortest paths in mere fractions of a second on continental sized road networks. In the presence of unreliability, however, current algorithms fail to achieve resu ..."
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Abstract. Computing shortest paths is one of the most researched topics in algorithm engineering. Currently available algorithms compute shortest paths in mere fractions of a second on continental sized road networks. In the presence of unreliability, however, current algorithms fail to achieve results as impressive as for the static setting. In contrast to speedup techniques for static route planning, current implementations for the stochastic ontime arrival problem require the computationally expensive step of solving convolution products. Running times can reach hours when considering large scale networks. We present a novel approach to reduce this immense computational effort of stochastic routing based on existing techniques for alternative routes. In an extensive experimental study, we show that the process of stochastic route planning can be speedup immensely, without sacrificing much in terms of accuracy. 1