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Documents authored by Sauer, Jonas

Document
DOI: 10.4230/LIPIcs.SEA.2023.16
Arc-Flags Meet Trip-Based Public Transit Routing

Authors: Ernestine Großmann, Jonas Sauer, Christian Schulz, and Patrick Steil

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)

Abstract
We present Arc-Flag TB, a journey planning algorithm for public transit networks which combines Trip-Based Public Transit Routing (TB) with the Arc-Flags speedup technique. Compared to previous attempts to apply Arc-Flags to public transit networks, which saw limited success, our approach uses stronger pruning rules to reduce the search space. Our experiments show that Arc-Flag TB achieves a speedup of up to two orders of magnitude over TB, offering query times of less than a millisecond even on large countrywide networks. Compared to the state-of-the-art speedup technique Trip-Based Public Transit Routing Using Condensed Search Trees (TB-CST), our algorithm achieves similar query times but requires significantly less additional memory. Other state-of-the-art algorithms which achieve even faster query times, e.g., Public Transit Labeling, require enormous memory usage. In contrast, Arc-Flag TB offers a tradeoff between query performance and memory usage due to the fact that the number of regions in the network partition required by our algorithm is a configurable parameter. We also identify a previously undiscovered issue in the transfer precomputation of TB, which causes both TB-CST and Arc-Flag TB to answer some queries incorrectly. We provide discussion on how to resolve this issue in the future. Currently, Arc-Flag TB answers 1-6% of queries incorrectly, compared to over 20% for TB-CST on some networks.
Cite as

Ernestine Großmann, Jonas Sauer, Christian Schulz, and Patrick Steil. Arc-Flags Meet Trip-Based Public Transit Routing. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gromann_et_al:LIPIcs.SEA.2023.16,
  author =	{Gro{\ss}mann, Ernestine and Sauer, Jonas and Schulz, Christian and Steil, Patrick},
  title =	{{Arc-Flags Meet Trip-Based Public Transit Routing}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.16},
  URN =		{urn:nbn:de:0030-drops-183664},
  doi =		{10.4230/LIPIcs.SEA.2023.16},
  annote =	{Keywords: Public transit routing, graph algorithms, algorithm engineering}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2022.14
Efficient Algorithms for Fully Multimodal Journey Planning

Authors: Moritz Potthoff and Jonas Sauer

Published in: OASIcs, Volume 106, 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)

Abstract
We study the journey planning problem for fully multimodal networks consisting of public transit and an arbitrary number of non-schedule-based transfer modes (e.g., walking, e-scooter, bicycle). Obtaining reasonable results in this setting requires multicriteria optimization, making the problem highly complex. Previous approaches were either limited to a single transfer mode or suffered from prohibitively slow running times. We establish a fully multimodal journey planning model that excludes undesirable solutions and can be solved efficiently. We extend existing efficient bimodal algorithms to our model and propose a new algorithm, HydRA, which enables even faster queries. On metropolitan and mid-sized country networks with walking and e-scooter as transfer modes, HydRA achieves query times of around 30 ms, which is fast enough for interactive applications.
Cite as

Moritz Potthoff and Jonas Sauer. Efficient Algorithms for Fully Multimodal Journey Planning. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{potthoff_et_al:OASIcs.ATMOS.2022.14,
  author =	{Potthoff, Moritz and Sauer, Jonas},
  title =	{{Efficient Algorithms for Fully Multimodal Journey Planning}},
  booktitle =	{22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)},
  pages =	{14:1--14:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-259-4},
  ISSN =	{2190-6807},
  year =	{2022},
  volume =	{106},
  editor =	{D'Emidio, Mattia and Lindner, Niels},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2022.14},
  URN =		{urn:nbn:de:0030-drops-171181},
  doi =		{10.4230/OASIcs.ATMOS.2022.14},
  annote =	{Keywords: Algorithms, Journey Planning, Multimodal, Multicriteria, Public Transit}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2020.1
An Efficient Solution for One-To-Many Multi-Modal Journey Planning

Authors: Jonas Sauer, Dorothea Wagner, and Tobias Zündorf

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

Abstract
We study the one-to-many journey planning problem in multi-modal transportation networks consisting of a public transit network and an additional, non-schedule-based mode of transport. Given a departure time and a single source vertex, we aim to compute optimal journeys to all vertices in a set of targets, optimizing both travel time and the number of transfers used. Solving this problem yields a crucial component in many other problems, such as efficient point-of-interest queries, computation of isochrones, or multi-modal traffic assignments. While many algorithms for multi-modal journey planning exist, none of them are applicable to one-to-many scenarios. Our solution is based on the combination of two state-of-the-art approaches: ULTRA, which enables efficient journey planning in multi-modal networks, but only for one-to-one queries, and (R)PHAST, which enables efficient one-to-many queries, but only in time-independent networks. Similarly to ULTRA, our new approach can be combined with any existing public transit algorithm that allows a search to all stops, which we demonstrate for CSA and RAPTOR. For small to moderately sized target sets, the resulting algorithms are nearly as fast as the pure public transit algorithms they are based on. For large target sets, we achieve a speedup of up to 7 compared to a naive one-to-many extension of a state-of-the-art multi-modal approach.
Cite as

Jonas Sauer, Dorothea Wagner, and Tobias Zündorf. An Efficient Solution for One-To-Many Multi-Modal Journey Planning. In 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020). Open Access Series in Informatics (OASIcs), Volume 85, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{sauer_et_al:OASIcs.ATMOS.2020.1,
  author =	{Sauer, Jonas and Wagner, Dorothea and Z\"{u}ndorf, Tobias},
  title =	{{An Efficient Solution for One-To-Many Multi-Modal Journey Planning}},
  booktitle =	{20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020)},
  pages =	{1:1--1:15},
  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.2020.1},
  URN =		{urn:nbn:de:0030-drops-131371},
  doi =		{10.4230/OASIcs.ATMOS.2020.1},
  annote =	{Keywords: Algorithm Engineering, Route Planning, Public Transit, One-to-Many}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2020.4
Integrating ULTRA and Trip-Based Routing

Authors: Jonas Sauer, Dorothea Wagner, and Tobias Zündorf

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

Abstract
We study a bi-modal journey planning scenario consisting of a public transit network and a transfer graph representing a secondary transportation mode (e.g., walking or cycling). Given a pair of source and target locations, the objective is to find a Pareto set of journeys optimizing arrival time and the number of required transfers. For public transit networks with a restricted, transitively closed transfer graph, one of the fastest known algorithms solving this bi-criteria problem is Trip-Based Routing [Witt, 2015]. However, this algorithm cannot be trivially extended to unrestricted transfer graphs. In this work, we combine Trip-Based Routing with ULTRA [Baum et al., 2019], a preprocessing technique that allows any public transit algorithm that requires transitive transfers to handle an unrestricted transfer graph. Since both ULTRA and Trip-Based Routing precompute transfer shortcuts in a preprocessing phase, a naive combination of the two leads to a three-phase algorithm that performs redundant work and produces superfluous shortcuts. We therefore propose a new, integrated preprocessing phase that combines the advantages of both and reduces the number of computed shortcuts by up to a factor of 9 compared to a naive combination. The resulting query algorithm, ULTRA-Trip-Based is the fastest known algorithm for the considered problem setting, achieving a speedup of up to 4 compared to the fastest previously known approach, ULTRA-RAPTOR.
Cite as

Jonas Sauer, Dorothea Wagner, and Tobias Zündorf. Integrating ULTRA and Trip-Based Routing. In 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020). Open Access Series in Informatics (OASIcs), Volume 85, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{sauer_et_al:OASIcs.ATMOS.2020.4,
  author =	{Sauer, Jonas and Wagner, Dorothea and Z\"{u}ndorf, Tobias},
  title =	{{Integrating ULTRA and Trip-Based Routing}},
  booktitle =	{20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020)},
  pages =	{4:1--4:15},
  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.2020.4},
  URN =		{urn:nbn:de:0030-drops-131408},
  doi =		{10.4230/OASIcs.ATMOS.2020.4},
  annote =	{Keywords: Algorithms, Journey Planning, Multi-Modal, Public Transportation}
}
Document
DOI: 10.4230/LIPIcs.SEA.2020.16
Faster Multi-Modal Route Planning With Bike Sharing Using ULTRA

Authors: Jonas Sauer, Dorothea Wagner, and Tobias Zündorf

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

Abstract
We study multi-modal route planning in a network comprised of schedule-based public transportation, unrestricted walking, and cycling with bikes available from bike sharing stations. So far this problem has only been considered for scenarios with at most one bike sharing operator, for which MCR is the best known algorithm [Delling et al., 2013]. However, for practical applications, algorithms should be able to distinguish between bike sharing stations of multiple competing bike sharing operators. Furthermore, MCR has recently been outperformed by ULTRA for multi-modal route planning scenarios without bike sharing [Baum et al., 2019]. In this paper, we present two approaches for modeling multi-modal transportation networks with multiple bike sharing operators: The operator-dependent model requires explicit handling of bike sharing stations within the algorithm, which we demonstrate with an adapted version of MCR. In the operator-expanded model, all relevant information is encoded within an expanded network. This allows for applying any multi-modal public transit algorithm without modification, which we show for ULTRA. We proceed by describing an additional preprocessing step called operator pruning, which can be used to accelerate both approaches. We conclude our work with an extensive experimental evaluation on the networks of London, Switzerland, and Germany. Our experiments show that the new preprocessing technique accelerates both approaches significantly, with the fastest algorithm (ULTRA-RAPTOR with operator pruning) being more than an order of magnitude faster than the basic MCR approach. Moreover, the ULTRA preprocessing step also benefits from operator pruning, as its running time is reduced by a factor of 14 to 20.
Cite as

Jonas Sauer, Dorothea Wagner, and Tobias Zündorf. Faster Multi-Modal Route Planning With Bike Sharing Using ULTRA. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{sauer_et_al:LIPIcs.SEA.2020.16,
  author =	{Sauer, Jonas and Wagner, Dorothea and Z\"{u}ndorf, Tobias},
  title =	{{Faster Multi-Modal Route Planning With Bike Sharing Using ULTRA}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{16:1--16:14},
  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.2020.16},
  URN =		{urn:nbn:de:0030-drops-120905},
  doi =		{10.4230/LIPIcs.SEA.2020.16},
  annote =	{Keywords: Algorithms, Route Planning, Bike Sharing, Public Transportation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.14
UnLimited TRAnsfers for Multi-Modal Route Planning: An Efficient Solution

Authors: Moritz Baum, Valentin Buchhold, Jonas Sauer, Dorothea Wagner, and Tobias Zündorf

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We study a multi-modal route planning scenario consisting of a public transit network and a transfer graph representing a secondary transportation mode (e.g., walking or taxis). The objective is to compute all journeys that are Pareto-optimal with respect to arrival time and the number of required transfers. While various existing algorithms can efficiently compute optimal journeys in either a pure public transit network or a pure transfer graph, combining the two increases running times significantly. As a result, even walking between stops is typically limited by a maximal duration or distance, or by requiring the transfer graph to be transitively closed. To overcome these shortcomings, we propose a novel preprocessing technique called ULTRA (UnLimited TRAnsfers): Given a complete transfer graph (without any limitations, representing an arbitrary non-schedule-based mode of transportation), we compute a small number of transfer shortcuts that are provably sufficient for computing all Pareto-optimal journeys. We demonstrate the practicality of our approach by showing that these transfer shortcuts can be integrated into a variety of state-of-the-art public transit algorithms, establishing the ULTRA-Query algorithm family. Our extensive experimental evaluation shows that ULTRA is able to improve these algorithms from limited to unlimited transfers without sacrificing query speed, yielding the fastest known algorithms for multi-modal routing. This is true not just for walking, but also for other transfer modes such as cycling or driving.
Cite as

Moritz Baum, Valentin Buchhold, Jonas Sauer, Dorothea Wagner, and Tobias Zündorf. UnLimited TRAnsfers for Multi-Modal Route Planning: An Efficient Solution. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{baum_et_al:LIPIcs.ESA.2019.14,
  author =	{Baum, Moritz and Buchhold, Valentin and Sauer, Jonas and Wagner, Dorothea and Z\"{u}ndorf, Tobias},
  title =	{{UnLimited TRAnsfers for Multi-Modal Route Planning: An Efficient Solution}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.14},
  URN =		{urn:nbn:de:0030-drops-111352},
  doi =		{10.4230/LIPIcs.ESA.2019.14},
  annote =	{Keywords: Algorithms, Optimization, Route Planning, Public Transportation}
}
Document
DOI: 10.4230/LIPIcs.SEA.2017.19
Consumption Profiles in Route Planning for Electric Vehicles: Theory and Applications

Authors: Moritz Baum, Jonas Sauer, Dorothea Wagner, and Tobias Zündorf

Published in: LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017)

Abstract
In route planning for electric vehicles (EVs), consumption profiles are a functional representation of optimal energy consumption between two locations, subject to initial state of charge. Efficient computation of profiles is a relevant problem on its own, but also a fundamental ingredient to many route planning approaches for EVs. In this work, we show that the complexity of a profile is at most linear in the graph size. Based on this insight, we derive a polynomial-time algorithm for the problem of finding an energy-optimal path between two locations that allows stops at charging stations. Exploiting efficient profile search, our approach also allows partial recharging at charging stations to save energy. In a sense, our results close the gap between efficient techniques for energy-optimal routes (based on simpler models) and NP-hard time-constrained problems involving charging stops for EVs. We propose a practical implementation, which we carefully integrate with Contraction Hierarchies and A* search. Even though the practical variant formally drops correctness, a comprehensive experimental study on a realistic, large-scale road network reveals that it always finds the optimal solution in our tests and computes even long-distance routes with charging stops in less than 300 ms.
Cite as

Moritz Baum, Jonas Sauer, Dorothea Wagner, and Tobias Zündorf. Consumption Profiles in Route Planning for Electric Vehicles: Theory and Applications. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{baum_et_al:LIPIcs.SEA.2017.19,
  author =	{Baum, Moritz and Sauer, Jonas and Wagner, Dorothea and Z\"{u}ndorf, Tobias},
  title =	{{Consumption Profiles in Route Planning for Electric Vehicles: Theory and Applications}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-036-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{75},
  editor =	{Iliopoulos, Costas S. and Pissis, Solon P. and Puglisi, Simon J. and Raman, Rajeev},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.19},
  URN =		{urn:nbn:de:0030-drops-76088},
  doi =		{10.4230/LIPIcs.SEA.2017.19},
  annote =	{Keywords: electric vehicles, charging station, shortest paths, route planning, profile search, algorithm engineering}
}
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