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Documents authored by Zeitz, Tim

Document
DOI: 10.4230/LIPIcs.ESA.2022.89
Combining Predicted and Live Traffic with Time-Dependent A* Potentials

Authors: Nils Werner and Tim Zeitz

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
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.
Cite as

Nils Werner and Tim Zeitz. Combining Predicted and Live Traffic with Time-Dependent A* Potentials. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 89:1-89:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{werner_et_al:LIPIcs.ESA.2022.89,
  author =	{Werner, Nils and Zeitz, Tim},
  title =	{{Combining Predicted and Live Traffic with Time-Dependent A* Potentials}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{89:1--89:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.89},
  URN =		{urn:nbn:de:0030-drops-170271},
  doi =		{10.4230/LIPIcs.ESA.2022.89},
  annote =	{Keywords: realistic road networks, shortest paths, live traffic, time-dependent routing}
}
Document
DOI: 10.4230/LIPIcs.SEA.2022.3
Fast Computation of Shortest Smooth Paths and Uniformly Bounded Stretch with Lazy RPHAST

Authors: Tim Zeitz

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
We study the shortest smooth path problem (SSPP), which is motivated by traffic-aware routing in road networks. The goal is to compute the fastest route according to the current traffic situation while avoiding undesired detours, such as briefly using a parking area to bypass a jammed highway. Detours are prevented by limiting the uniformly bounded stretch (UBS) with respect to a second weight function which disregards the traffic situation. The UBS is a path quality metric which measures the maximum relative length of detours on a path. In this paper, we settle the complexity of the SSPP and show that it is strongly NP-complete. We then present practical algorithms to solve the problem on continental-sized road networks both heuristically and exactly. A crucial building block of these algorithms is the UBS evaluation. We propose a novel algorithm to compute the UBS with only a few shortest path computations on typical paths. All our algorithms utilize Lazy RPHAST, a recently proposed technique to incrementally compute distances from many vertices towards a common target. An extensive evaluation shows that our algorithms outperform competing SSPP algorithms by up to two orders of magnitude and that our new UBS algorithm is the first to consistently compute exact UBS values in a matter of milliseconds.
Cite as

Tim Zeitz. Fast Computation of Shortest Smooth Paths and Uniformly Bounded Stretch with Lazy RPHAST. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{zeitz:LIPIcs.SEA.2022.3,
  author =	{Zeitz, Tim},
  title =	{{Fast Computation of Shortest Smooth Paths and Uniformly Bounded Stretch with Lazy RPHAST}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.3},
  URN =		{urn:nbn:de:0030-drops-165378},
  doi =		{10.4230/LIPIcs.SEA.2022.3},
  annote =	{Keywords: realistic road networks, route planning, shortest paths, traffic-aware routing, live traffic, uniformly bounded stretch}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.6
A Fast and Tight Heuristic for A* in Road Networks

Authors: Ben Strasser and Tim Zeitz

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)

Abstract
We study exact, efficient and practical algorithms for route planning in large road networks. Routing applications often require integrating the current traffic situation, planning ahead with traffic predictions for the future, respecting forbidden turns, and many other features depending on the exact application. While Dijkstra’s algorithm can be used to solve these problems, it is too slow for many applications. A* is a classical approach to accelerate Dijkstra’s algorithm. A* can support many extended scenarios without much additional implementation complexity. However, A*’s performance depends on the availability of a good heuristic that estimates distances. Computing tight distance estimates is a challenge on its own. On road networks, shortest paths can also be quickly computed using hierarchical speedup techniques. They achieve speed and exactness but sacrifice A*’s flexibility. Extending them to certain practical applications can be hard. In this paper, we present an algorithm to efficiently extract distance estimates for A* from Contraction Hierarchies (CH), a hierarchical technique. We call our heuristic CH-Potentials. Our approach allows decoupling the supported extensions from the hierarchical speed-up technique. Additionally, we describe A* optimizations to accelerate the processing of low degree nodes, which often occur in road networks.
Cite as

Ben Strasser and Tim Zeitz. A Fast and Tight Heuristic for A* in Road Networks. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{strasser_et_al:LIPIcs.SEA.2021.6,
  author =	{Strasser, Ben and Zeitz, Tim},
  title =	{{A Fast and Tight Heuristic for A* in Road Networks}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.6},
  URN =		{urn:nbn:de:0030-drops-137780},
  doi =		{10.4230/LIPIcs.SEA.2021.6},
  annote =	{Keywords: route planning, shortest paths, realistic road networks}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2020.9
Customizable Contraction Hierarchies with Turn Costs

Authors: Valentin Buchhold, Dorothea Wagner, Tim Zeitz, and Michael Zündorf

Published in: OASIcs, Volume 85, 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020)

Abstract
We incorporate turn restrictions and turn costs into the route planning algorithm customizable contraction hierarchies (CCH). There are two common ways to represent turn costs and restrictions. The edge-based model expands the network so that road segments become vertices and allowed turns become edges. The compact model keeps intersections as vertices, but associates a turn table with each vertex. Although CCH can be used as is on the edge-based model, the performance of preprocessing and customization is severely affected. While the expanded network is only three times larger, both preprocessing and customization time increase by up to an order of magnitude. In this work, we carefully engineer CCH to exploit different properties of the expanded graph. We reduce the increase in customization time from up to an order of magnitude to a factor of about 3. The increase in preprocessing time is reduced even further. Moreover, we present a CCH variant that works on the compact model, and show that it performs worse than the variant on the edge-based model. Surprisingly, the variant on the edge-based model even uses less space than the one on the compact model, although the compact model was developed to keep the space requirement low.
Cite as

Valentin Buchhold, Dorothea Wagner, Tim Zeitz, and Michael Zündorf. Customizable Contraction Hierarchies with Turn Costs. In 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020). Open Access Series in Informatics (OASIcs), Volume 85, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{buchhold_et_al:OASIcs.ATMOS.2020.9,
  author =	{Buchhold, Valentin and Wagner, Dorothea and Zeitz, Tim and Z\"{u}ndorf, Michael},
  title =	{{Customizable Contraction Hierarchies with Turn Costs}},
  booktitle =	{20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020)},
  pages =	{9:1--9:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-170-2},
  ISSN =	{2190-6807},
  year =	{2020},
  volume =	{85},
  editor =	{Huisman, Dennis and Zaroliagis, Christos D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2020.9},
  URN =		{urn:nbn:de:0030-drops-131453},
  doi =		{10.4230/OASIcs.ATMOS.2020.9},
  annote =	{Keywords: Turn costs, realistic road networks, customizable contraction hierarchies, route planning, shortest paths}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.81
Space-Efficient, Fast and Exact Routing in Time-Dependent Road Networks

Authors: Ben Strasser, Dorothea Wagner, and Tim Zeitz

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
We study the problem of computing 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 either 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 30 times smaller indexes than competing approaches.
Cite as

Ben Strasser, Dorothea Wagner, and Tim Zeitz. Space-Efficient, Fast and Exact Routing in Time-Dependent Road Networks. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 81:1-81:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{strasser_et_al:LIPIcs.ESA.2020.81,
  author =	{Strasser, Ben and Wagner, Dorothea and Zeitz, Tim},
  title =	{{Space-Efficient, Fast and Exact Routing in Time-Dependent Road Networks}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{81:1--81:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.81},
  URN =		{urn:nbn:de:0030-drops-129479},
  doi =		{10.4230/LIPIcs.ESA.2020.81},
  annote =	{Keywords: realistic road networks, time-dependent route planning, shortest paths}
}
Document
DOI: 10.4230/LIPIcs.SEA.2020.17
Efficient Route Planning with Temporary Driving Bans, Road Closures, and Rated Parking Areas

Authors: Alexander Kleff, Frank Schulz, Jakob Wagenblatt, and Tim Zeitz

Published in: LIPIcs, Volume 160, 18th International Symposium on Experimental Algorithms (SEA 2020)

Abstract
We study the problem of planning routes in road networks when certain streets or areas are closed at certain times. For heavy vehicles, such areas may be very large since many European countries impose temporary driving bans during the night or on weekends. In this setting, feasible routes may require waiting at parking areas, and several feasible routes with different trade-offs between waiting and driving detours around closed areas may exist. We propose a novel model in which driving and waiting are assigned abstract costs, and waiting costs are location-dependent to reflect the different quality of the parking areas. Our goal is to find Pareto-optimal routes with regards to arrival time at the destination and total cost. We investigate the complexity of the model and determine a necessary constraint on the cost parameters such that the problem is solvable in polynomial time. We present a thoroughly engineered implementation and perform experiments on a production-grade real world data set. The experiments show that our implementation can answer realistic queries in around a second or less which makes it feasible for practical application.
Cite as

Alexander Kleff, Frank Schulz, Jakob Wagenblatt, and Tim Zeitz. Efficient Route Planning with Temporary Driving Bans, Road Closures, and Rated Parking Areas. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 17:1-17:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kleff_et_al:LIPIcs.SEA.2020.17,
  author =	{Kleff, Alexander and Schulz, Frank and Wagenblatt, Jakob and Zeitz, Tim},
  title =	{{Efficient Route Planning with Temporary Driving Bans, Road Closures, and Rated Parking Areas}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{17:1--17:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Faro, Simone and Cantone, Domenico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2020.17},
  URN =		{urn:nbn:de:0030-drops-120910},
  doi =		{10.4230/LIPIcs.SEA.2020.17},
  annote =	{Keywords: driving bans, realistic road networks, route planning, shortest paths}
}
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