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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 time-dependent edge weights. This is the first hierarchical speedup technique for time-dependent 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 time-dependent edge weights. This is the first hierarchical speedup technique for time-dependent routing that allows bidirectional query algorithms. 1
Efficient Route Planning in Flight Networks
, 2009
"... We present a set of three new time-dependent 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 time-dependent 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 time-dependent shortest path computation in spatial networks
- IN: PROC. OF THE SIGSPATIAL INTL. CONF. ON ADVANCES IN GIS
, 2010
"... The problem of point-to-point shortest path computation in spatial networks is extensively studied with many approaches proposed to speed-up the computation. Most of the existing approaches make the simplifying assumption that weights (e.g., travel-time) of the network edges are constant. However, w ..."
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The problem of point-to-point shortest path computation in spatial networks is extensively studied with many approaches proposed to speed-up the computation. Most of the existing approaches make the simplifying assumption that weights (e.g., travel-time) of the network edges are constant. However, with real-world spatial networks the edge travel-times are time-dependent, where the arrivaltime to an edge determines the actual travel-time of the edge. With this paper, we study the applicability of existing shortest path algorithms to real-world large time-dependent spatial networks. In addition, we evaluate the importance of considering time-dependent edge travel-times for route planning in spatial networks. We show that time-dependent shortest path computation can reduce the traveltime by 36 % on average as compared to the static shortest path computation that assumes constant edge travel-times.
Core Routing on Dynamic Time-Dependent Road Networks
, 2010
"... Route planning in large scale time-dependent road networks is an important practical application of the shortest paths problem that greatly benefits from speedup techniques. In this paper we extend a two-level hierarchical approach for pointto-point shortest paths computations to the time-dependent ..."
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Route planning in large scale time-dependent road networks is an important practical application of the shortest paths problem that greatly benefits from speedup techniques. In this paper we extend a two-level hierarchical approach for pointto-point shortest paths computations to the time-dependent 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 goal-directed 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 time-dependent arc costs are not fixed, but can have their coefficients updated requiring only a small computational effort.
Distance Oracles for Time-Dependent Networks
"... Abstract. We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO prop-erty. Our approach precomputes (1 + ε)−approximate distance sum-maries from selected la ..."
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Abstract. We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO prop-erty. Our approach precomputes (1 + ε)−approximate distance sum-maries from selected landmark vertices to all other vertices in the network, and provides two sublinear-time query algorithms that deliver constant and (1+σ)−approximate shortest-travel-times, respectively, for arbitrary origin-destination pairs in the network. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about travel-time functions which allow the smooth transition towards asymmetric and time-dependent distance metrics. 1
Pruning Techniques for the Stochastic on-time 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 speed-up techniques for static route planning, current implementations for the stochastic on-time 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 speed-up immensely, without sacrificing much in terms of accuracy. 1
