Faster and Better Nested Dissection Orders for Customizable Contraction Hierarchies

Gottesbüren, Lars; Hamann, Michael; Uhl, Tim Niklas; Wagner, Dorothea

doi:10.3390/a12090196

Cited by 9 publications

(4 citation statements)

References 30 publications

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“…Also, the customization can be parallelized internally. For further engineering details, we refer to [7,4,12].…”

Section: Multi-metric Potentialsmentioning

confidence: 99%

Combining Predicted and Live Traffic with Time-Dependent A* Potentials

Werner,

Zeitz

2022

Preprint

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We study efficient and exact shortest path algorithms for routing on road networks with realistic traffic data. For navigation applications, both current (i.e., live) traffic events and predictions of future traffic flows play an important role in routing. While preprocessing-based speedup techniques have been employed successfully to both settings individually, a combined model poses significant challenges. Supporting predicted traffic typically requires expensive preprocessing while live traffic requires fast updates for regular adjustments. We propose an A*-based solution to this problem. By generalizing A* potentials to time dependency, i.e. the estimate of the distance from a vertex to the target also depends on the time of day when the vertex is visited, we achieve significantly faster query times than previously possible. Our evaluation shows that our approach enables interactive query times on continental-sized road networks while allowing live traffic updates within a fraction of a minute. We achieve a speedup of at least two orders of magnitude over Dijkstra's algorithm and up to one order of magnitude over state-of-the-art time-independent A* potentials.

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“…Also, the customization can be parallelized internally. For further engineering details, we refer to [7,4,12].…”

Section: Multi-metric Potentialsmentioning

confidence: 99%

Combining Predicted and Live Traffic with Time-Dependent A* Potentials

Werner,

Zeitz

2022

Preprint

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“…Since no travel time functions are involved, we can adapt the algorithms of Dibbelt et al [5] without modification. We use InertialFlowCutter [26] to obtain the nested dissection order. To generate the augmented graph, we implement an improved contraction algorithm first presented in [27].…”

Section: Preprocessingmentioning

confidence: 99%

“…We now focus on the second preprocessing phase. The first preprocessing phase does not use any time-dependent information and only reuses existing algorithms which have been evaluated in greater detail in other works [26,27]. For the scope of this subsection, we only use the Eur20 graph.…”

Section: Customizationmentioning

confidence: 99%

Space-Efficient, Fast and Exact Routing in Time-Dependent Road Networks

2021

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We study the problem of quickly computing point-to-point shortest paths in massive road networks with traffic predictions. Incorporating traffic predictions into routing allows, for example, to avoid commuter traffic congestions. Existing techniques follow a two-phase approach: In a preprocessing step, an index is built. The index depends on the road network and the traffic patterns but not on the path start and end. The latter are the input of the query phase, in which shortest paths are computed. All existing techniques have large index size, slow query running times or may compute suboptimal paths. In this work, we introduce CATCHUp (Customizable Approximated Time-dependent Contraction Hierarchies through Unpacking), the first algorithm that simultaneously achieves all three objectives. The core idea of CATCHUp is to store paths instead of travel times at shortcuts. Shortcut travel times are derived lazily from the stored paths. We perform an experimental study on a set of real world instances and compare our approach with state-of-the-art techniques. Our approach achieves the fastest preprocessing, competitive query running times and up to 38 times smaller indexes than competing approaches.

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“…, G d should be balanced. Therefore, separator decompositions are typically obtained by recursive dissection (e.g., using Inertial Flow [36], FlowCutter [27], or InertialFlowCutter [25]).…”

Section: Preliminariesmentioning

confidence: 99%

Nearest-Neighbor Queries in Customizable Contraction Hierarchies and Applications

Buchhold¹,

Wagner²

2021

Preprint

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Customizable contraction hierarchies are one of the most popular route planning frameworks in practice, due to their simplicity and versatility. In this work, we present a novel algorithm for finding k-nearest neighbors in customizable contraction hierarchies by systematically exploring the associated separator decomposition tree. Compared to previous bucket-based approaches, our algorithm requires much less target-dependent preprocessing effort. Moreover, we use our novel approach in two concrete applications. The first application are online k-closest point-of-interest queries, where the points of interest are only revealed at query time. We achieve query times of about 25 milliseconds on a continental road network, which is fast enough for interactive systems. The second application is travel demand generation. We show how to accelerate a recently introduced travel demand generator by a factor of more than 50 using our novel nearest-neighbor algorithm.

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Faster and Better Nested Dissection Orders for Customizable Contraction Hierarchies

Cited by 9 publications

References 30 publications

Combining Predicted and Live Traffic with Time-Dependent A* Potentials

Combining Predicted and Live Traffic with Time-Dependent A* Potentials

Space-Efficient, Fast and Exact Routing in Time-Dependent Road Networks

Nearest-Neighbor Queries in Customizable Contraction Hierarchies and Applications

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