9 Search Results for "Pajor, Thomas"

Document
DOI: 10.4230/OASIcs.ATMOS.2025.13
Multi-Criteria Route Planning with Little Regret

Authors: Carina Truschel and Sabine Storandt

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract
Multi-criteria route planning arises naturally in real-world navigation scenarios where users care about more than just one objective - such as minimizing travel time while also avoiding steep inclines or unpaved surfaces or toll routes. To capture the possible trade-offs between competing criteria, many algorithms compute the set of Pareto-optimal paths, which are paths that are not dominated by others with respect to the considered cost vectors. However, the number of Pareto-optimal paths can grow exponentially with the size of the input graph. This leads to significant computational overhead and results in large output sets that overwhelm users with too many alternatives. In this work, we present a technique based on the notion of regret minimization that efficiently filters the Pareto set during or after the search to a subset of specified size. Regret minimizing algorithms identify such a representative solution subset by considering how any possible user values any subset with respect to the objectives. We prove that regret-based filtering provides us with quality guarantees for the two main query types that are considered in the context of multi-criteria route planning, namely constrained shortest path queries and personalized path queries. Furthermore, we design a novel regret minimization algorithm that works for any number of criteria, is easy to implement and produces solutions with much smaller regret value than the most commonly used baseline algorithm. We carefully describe how to incorporate our regret minimization algorithm into existing route planning techniques to drastically reduce their running times and space consumption, while still returning paths that are close-to-optimal.
Cite as

Carina Truschel and Sabine Storandt. Multi-Criteria Route Planning with Little Regret. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{truschel_et_al:OASIcs.ATMOS.2025.13,
  author =	{Truschel, Carina and Storandt, Sabine},
  title =	{{Multi-Criteria Route Planning with Little Regret}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{13:1--13:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2025.13},
  URN =		{urn:nbn:de:0030-drops-247698},
  doi =		{10.4230/OASIcs.ATMOS.2025.13},
  annote =	{Keywords: Pareto-optimality, Regret minimization, Contraction Hierarchies}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2025.12
Separator-Based Alternative Paths in Customizable Contraction Hierarchies

Authors: Scott Bacherle, Thomas Bläsius, and Michael Zündorf

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract
We propose an algorithm for computing alternatives to the shortest path in a road network, based on the speed-up technique CCH (customizable contraction hierarchy). Computing alternative paths is a well-studied problem, motivated by the fact that route-planning applications benefit from presenting different high-quality options the user can choose from. Another crucial feature of modern routing applications is the inclusion of live traffic, which requires speed-up techniques that allow efficient metric updates. Besides CCH, the other speed-up technique supporting metric updates is CRP (customizable route planning). Of the two, CCH is the more modern solution with the advantages of providing faster queries and being substantially simpler to implement efficiently. However, so far, CCH has been lacking a way of computing alternative paths. While for CRP, the commonly used plateau method for computing alternatives can be applied, this is not so straightforward for CCH. With this paper, we make CCH a viable option for alternative paths, by proposing a new separator-based approach to computing alternative paths that works hand-in-hand with the CCH data structure. With our experiments, we demonstrate that CCH can indeed be used to compute alternative paths efficiently. With this, we provide an alternative to CRP that is simpler and has lower query times.
Cite as

Scott Bacherle, Thomas Bläsius, and Michael Zündorf. Separator-Based Alternative Paths in Customizable Contraction Hierarchies. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bacherle_et_al:OASIcs.ATMOS.2025.12,
  author =	{Bacherle, Scott and Bl\"{a}sius, Thomas and Z\"{u}ndorf, Michael},
  title =	{{Separator-Based Alternative Paths in Customizable Contraction Hierarchies}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{12:1--12:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2025.12},
  URN =		{urn:nbn:de:0030-drops-247685},
  doi =		{10.4230/OASIcs.ATMOS.2025.12},
  annote =	{Keywords: Alternative routes, realistic road networks, customizable contraction hierarchies, route planning, shortest paths}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.10
Algorithm Engineering of SSSP with Negative Edge Weights

Authors: Alejandro Cassis, Andreas Karrenbauer, André Nusser, and Paolo Luigi Rinaldi

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
Computing shortest paths is one of the most fundamental algorithmic graph problems. It is known since decades that this problem can be solved in near-linear time if all weights are nonnegative. A recent break-through by [Aaron Bernstein et al., 2022] presented a randomized near-linear time algorithm for this problem. A subsequent improvement in [Karl Bringmann et al., 2023] significantly reduced the number of logarithmic factors and thereby also simplified the algorithm. It is surprising and exciting that both of these algorithms are combinatorial and do not contain any fundamental obstacles for being practical. We launch the, to the best of our knowledge, first extensive investigation towards a practical implementation of [Karl Bringmann et al., 2023]. To this end, we give an accessible overview of the algorithm and discuss what adaptions are necessary to obtain a fast algorithm in practice. We manifest these adaptions in an efficient implementation. We test our implementation on a benchmark data set that is adapted to be more difficult for our implementation in order to allow for a fair comparison. As in [Karl Bringmann et al., 2023] as well as in our implementation there are multiple parameters to tune, we empirically evaluate their effect and thereby determine the best choices. Our implementation is then extensively compared to one of the state-of-the-art algorithms for this problem [Andrew V. Goldberg and Tomasz Radzik, 1993]. On the hardest instance type, we are faster by up to almost two orders of magnitude.
Cite as

Alejandro Cassis, Andreas Karrenbauer, André Nusser, and Paolo Luigi Rinaldi. Algorithm Engineering of SSSP with Negative Edge Weights. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cassis_et_al:LIPIcs.SEA.2025.10,
  author =	{Cassis, Alejandro and Karrenbauer, Andreas and Nusser, Andr\'{e} and Rinaldi, Paolo Luigi},
  title =	{{Algorithm Engineering of SSSP with Negative Edge Weights}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.10},
  URN =		{urn:nbn:de:0030-drops-232486},
  doi =		{10.4230/LIPIcs.SEA.2025.10},
  annote =	{Keywords: Single Source Shortest Paths, Negative Weights, Near-Linear Time}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2017.8
Faster Transit Routing by Hyper Partitioning

Authors: Daniel Delling, Julian Dibbelt, Thomas Pajor, and Tobias Zündorf

Published in: OASIcs, Volume 59, 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)

Abstract
We present a preprocessing-based acceleration technique for computing bi-criteria Pareto-optimal journeys in public transit networks, based on the well-known RAPTOR algorithm [Delling et al 2015]. Our key idea is to first partition a hypergraph into cells, in which vertices correspond to routes (e.g., bus lines) and hyperedges to stops, and to then mark routes sufficient for optimal travel across cells. The query can then be restricted to marked routes and those in the source and target cells. This results in a practical approach, suitable for networks that are too large to be efficiently handled by the basic RAPTOR algorithm.
Cite as

Daniel Delling, Julian Dibbelt, Thomas Pajor, and Tobias Zündorf. Faster Transit Routing by Hyper Partitioning. In 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017). Open Access Series in Informatics (OASIcs), Volume 59, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{delling_et_al:OASIcs.ATMOS.2017.8,
  author =	{Delling, Daniel and Dibbelt, Julian and Pajor, Thomas and Z\"{u}ndorf, Tobias},
  title =	{{Faster Transit Routing by Hyper Partitioning}},
  booktitle =	{17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)},
  pages =	{8:1--8:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-042-2},
  ISSN =	{2190-6807},
  year =	{2017},
  volume =	{59},
  editor =	{D'Angelo, Gianlorenzo and Dollevoet, Twan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2017.8},
  URN =		{urn:nbn:de:0030-drops-78962},
  doi =		{10.4230/OASIcs.ATMOS.2017.8},
  annote =	{Keywords: Routing, speed-up techniques, public transport, partitioning}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.1
Towards Realistic Pedestrian Route Planning

Authors: Simeon Andreev, Julian Dibbelt, Martin Nöllenburg, Thomas Pajor, and Dorothea Wagner

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
Pedestrian routing has its specific set of challenges, which are often neglected by state-of-the-art route planners. For instance, the lack of detailed sidewalk data and the inability to traverse plazas and parks in a natural way often leads to unappealing and suboptimal routes. In this work, we first propose to augment the network by generating sidewalks based on the street geometry and adding edges for routing over plazas and squares. Using this and further information, our query algorithm seamlessly handles node-to-node queries and queries whose origin or destination is an arbitrary location on a plaza or inside a park. Our experiments show that we are able to compute appealing pedestrian routes at negligible overhead over standard routing algorithms.
Cite as

Simeon Andreev, Julian Dibbelt, Martin Nöllenburg, Thomas Pajor, and Dorothea Wagner. Towards Realistic Pedestrian Route Planning. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{andreev_et_al:OASIcs.ATMOS.2015.1,
  author =	{Andreev, Simeon and Dibbelt, Julian and N\"{o}llenburg, Martin and Pajor, Thomas and Wagner, Dorothea},
  title =	{{Towards Realistic Pedestrian Route Planning}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{1--15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.1},
  URN =		{urn:nbn:de:0030-drops-54592},
  doi =		{10.4230/OASIcs.ATMOS.2015.1},
  annote =	{Keywords: pedestrian routing, realistic model, shortest paths, speed-up technique}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2014.138
Speed-Consumption Tradeoff for Electric Vehicle Route Planning

Authors: Moritz Baum, Julian Dibbelt, Lorenz Hübschle-Schneider, Thomas Pajor, and Dorothea Wagner

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Abstract
We study the problem of computing routes for electric vehicles (EVs) in road networks. Since their battery capacity is limited, and consumed energy per distance increases with velocity, driving the fastest route is often not desirable and may even be infeasible. On the other hand, the energy-optimal route may be too conservative in that it contains unnecessary detours or simply takes too long. In this work, we propose to use multicriteria optimization to obtain Pareto sets of routes that trade energy consumption for speed. In particular, we exploit the fact that the same road segment can be driven at different speeds within reasonable intervals. As a result, we are able to provide routes with low energy consumption that still follow major roads, such as freeways. Unfortunately, the size of the resulting Pareto sets can be too large to be practical. We therefore also propose several nontrivial techniques that can be applied on-line at query time in order to speed up computation and filter insignificant solutions from the Pareto sets. Our extensive experimental study, which uses a real-world energy consumption model, reveals that we are able to compute diverse sets of alternative routes on continental networks that closely resemble the exact Pareto set in just under a second---several orders of magnitude faster than the exhaustive algorithm.
Cite as

Moritz Baum, Julian Dibbelt, Lorenz Hübschle-Schneider, Thomas Pajor, and Dorothea Wagner. Speed-Consumption Tradeoff for Electric Vehicle Route Planning. In 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. 138-151, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{baum_et_al:OASIcs.ATMOS.2014.138,
  author =	{Baum, Moritz and Dibbelt, Julian and H\"{u}bschle-Schneider, Lorenz and Pajor, Thomas and Wagner, Dorothea},
  title =	{{Speed-Consumption Tradeoff for Electric Vehicle Route Planning}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{138--151},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014.138},
  URN =		{urn:nbn:de:0030-drops-47583},
  doi =		{10.4230/OASIcs.ATMOS.2014.138},
  annote =	{Keywords: electric vehicles, shortest paths, route planning, bicriteria optimization, algorithm engineering}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2011.64
UniALT for regular language contrained shortest paths on a multi-modal transportation network

Authors: Dominik Kirchler, Leo Liberti, Thomas Pajor, and Roberto Wolfler Calvo

Published in: OASIcs, Volume 20, 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2011)

Abstract
Shortest paths on road networks can be efficiently calculated using Dijkstra's algorithm (D). In addition to roads, multi-modal transportation networks include public transportation, bicycle lanes, etc. For paths on this type of network, further constraints, e.g., preferences in using certain modes of transportation, may arise. The regular language constrained shortest path problem deals with this kind of problem. It uses a regular language to model the constraints. The problem can be solved efficiently by using a generalization of Dijkstra's algorithm (D_RegLC). In this paper we propose an adaption of the speed-up technique uniALT, in order to accelerate D_RegLC. We call our algorithm SDALT. We provide experimental results on a realistic multi-modal public transportation network including time-dependent cost functions on arcs. The experiments show that our algorithm performs well, with speed-ups of a factor 2 to 20.
Cite as

Dominik Kirchler, Leo Liberti, Thomas Pajor, and Roberto Wolfler Calvo. UniALT for regular language contrained shortest paths on a multi-modal transportation network. In 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 20, pp. 64-75, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{kirchler_et_al:OASIcs.ATMOS.2011.64,
  author =	{Kirchler, Dominik and Liberti, Leo and Pajor, Thomas and Wolfler Calvo, Roberto},
  title =	{{UniALT for regular language contrained shortest paths on a multi-modal transportation network}},
  booktitle =	{11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{64--75},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-33-0},
  ISSN =	{2190-6807},
  year =	{2011},
  volume =	{20},
  editor =	{Caprara, Alberto and Kontogiannis, Spyros},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2011.64},
  URN =		{urn:nbn:de:0030-drops-32670},
  doi =		{10.4230/OASIcs.ATMOS.2011.64},
  annote =	{Keywords: time-dependency, ALT, regular language, shortest path, multi-modal}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2009.2145
Efficient Route Planning in Flight Networks

Authors: Daniel Delling, Thomas Pajor, Dorothea Wagner, and Christos Zaroliagis

Published in: OASIcs, Volume 12, 9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'09) (2009)

Abstract
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.
Cite as

Daniel Delling, Thomas Pajor, Dorothea Wagner, and Christos Zaroliagis. Efficient Route Planning in Flight Networks. In 9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'09). Open Access Series in Informatics (OASIcs), Volume 12, pp. 1-17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{delling_et_al:OASIcs.ATMOS.2009.2145,
  author =	{Delling, Daniel and Pajor, Thomas and Wagner, Dorothea and Zaroliagis, Christos},
  title =	{{Efficient Route Planning in Flight Networks}},
  booktitle =	{9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'09)},
  pages =	{1--17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-11-8},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{12},
  editor =	{Clausen, Jens and Di Stefano, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2009.2145},
  URN =		{urn:nbn:de:0030-drops-21450},
  doi =		{10.4230/OASIcs.ATMOS.2009.2145},
  annote =	{Keywords: Timetable information, flight modeling, shortest paths, multi criteria, table lookups Timetable information, flight modeling, shortest paths, multi criteria, table lookups}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2008.1582
Engineering Time-Expanded Graphs for Faster Timetable Information

Authors: Daniel Delling, Thomas Pajor, and Dorothea Wagner

Published in: OASIcs, Volume 9, 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08) (2008)

Abstract
We present an extension of the well-known time-expanded approach for timetable information. By remodeling unimportant stations, we are able to obtain faster query times with less space consumption than the original model. Moreover, we show that our extensions harmonize well with speed-up techniques whose adaption to timetable networks is more challenging than one might expect.
Cite as

Daniel Delling, Thomas Pajor, and Dorothea Wagner. Engineering Time-Expanded Graphs for Faster Timetable Information. In 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08). Open Access Series in Informatics (OASIcs), Volume 9, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{delling_et_al:OASIcs.ATMOS.2008.1582,
  author =	{Delling, Daniel and Pajor, Thomas and Wagner, Dorothea},
  title =	{{Engineering Time-Expanded Graphs for Faster Timetable Information}},
  booktitle =	{8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08)},
  pages =	{1--20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-07-1},
  ISSN =	{2190-6807},
  year =	{2008},
  volume =	{9},
  editor =	{Fischetti, Matteo and Widmayer, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2008.1582},
  URN =		{urn:nbn:de:0030-drops-15826},
  doi =		{10.4230/OASIcs.ATMOS.2008.1582},
  annote =	{Keywords: Timetable information, shortest path, modeling}
}
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