3 Search Results for "Dokka, Trivikram"

Document
DOI: 10.4230/LIPIcs.ESA.2025.34
On the Approximability of Train Routing and the Min-Max Disjoint Paths Problem

Authors: Umang Bhaskar, Katharina Eickhoff, Lennart Kauther, Jannik Matuschke, Britta Peis, and Laura Vargas Koch

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
In train routing, the headway is the minimum distance that must be maintained between successive trains for safety and robustness. We introduce a model for train routing that requires a fixed headway to be maintained between trains, and study the problem of minimizing the makespan, i.e., the arrival time of the last train, in a single-source single-sink network. For this problem, we first show that there exists an optimal solution where trains move in convoys - that is, the optimal paths for any two trains are either the same or are arc-disjoint. Via this insight, we are able to reduce the approximability of our train routing problem to that of the min-max disjoint paths problem, which asks for a collection of disjoint paths where the maximum length of any path in the collection is as small as possible. While min-max disjoint paths inherits a strong inapproximability result on directed acyclic graphs from the multi-level bottleneck assignment problem, we show that a natural greedy composition approach yields a logarithmic approximation in the number of disjoint paths for series-parallel graphs. We also present an alternative analysis of this approach that yields a guarantee depending on how often the decomposition tree of the series-parallel graph alternates between series and parallel compositions on any root-leaf path.
Cite as

Umang Bhaskar, Katharina Eickhoff, Lennart Kauther, Jannik Matuschke, Britta Peis, and Laura Vargas Koch. On the Approximability of Train Routing and the Min-Max Disjoint Paths Problem. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bhaskar_et_al:LIPIcs.ESA.2025.34,
  author =	{Bhaskar, Umang and Eickhoff, Katharina and Kauther, Lennart and Matuschke, Jannik and Peis, Britta and Vargas Koch, Laura},
  title =	{{On the Approximability of Train Routing and the Min-Max Disjoint Paths Problem}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.34},
  URN =		{urn:nbn:de:0030-drops-245029},
  doi =		{10.4230/LIPIcs.ESA.2025.34},
  annote =	{Keywords: Train Routing, Scheduling, Approximation Algorithms, Flows over Time, Min-Max Disjoint Paths}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2017.16
An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems

Authors: Trivikram Dokka and Marc Goerigk

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

Abstract
Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the network may not be known. This led to the development of robust shortest path problems, where all possible arc travel times are contained in a so-called uncertainty set of possible outcomes. Research in robust shortest path problems typically assumes this set to be given, and provides complexity results as well as algorithms depending on its shape. However, what can actually be observed in real-world problems are only discrete raw data points. The shape of the uncertainty is already a modelling assumption. In this paper we test several of the most widely used assumptions on the uncertainty set using real-world traffic measurements provided by the City of Chicago. We calculate the resulting different robust solutions, and evaluate which uncertainty approach is actually reasonable for our data. This anchors theoretical research in a real-world application and gives an indicator which robust models should be the future focus of algorithmic development.
Cite as

Trivikram Dokka and Marc Goerigk. An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems. In 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017). Open Access Series in Informatics (OASIcs), Volume 59, pp. 16:1-16:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{dokka_et_al:OASIcs.ATMOS.2017.16,
  author =	{Dokka, Trivikram and Goerigk, Marc},
  title =	{{An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems}},
  booktitle =	{17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)},
  pages =	{16:1--16:13},
  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.2017.16},
  URN =		{urn:nbn:de:0030-drops-79035},
  doi =		{10.4230/OASIcs.ATMOS.2017.16},
  annote =	{Keywords: robust shortest paths, uncertainty sets, real-world data, experimental study}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2016.4
Pricing Toll Roads under Uncertainty

Authors: Trivikram Dokka, Alain Zemkoho, Sonali Sen Gupta, and Fabrice Talla Nobibon

Published in: OASIcs, Volume 54, 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)

Abstract
We study the toll pricing problem when the non-toll costs on the network are not fixed and can vary over time. We assume that users who take their decisions, after the tolls are fixed, have full information of all costs before making their decision. Toll-setter, on the other hand, do not have any information of the future costs on the network. The only information toll-setter have is historical information (sample) of the network costs. In this work we study this problem on parallel networks and networks with few number of paths in single origin-destination setting. We formulate toll-setting problem in this setting as a distributionally robust optimization problem and propose a method to solve to it. We illustrate the usefulness of our approach by doing numerical experiments using a parallel network.
Cite as

Trivikram Dokka, Alain Zemkoho, Sonali Sen Gupta, and Fabrice Talla Nobibon. Pricing Toll Roads under Uncertainty. In 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016). Open Access Series in Informatics (OASIcs), Volume 54, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{dokka_et_al:OASIcs.ATMOS.2016.4,
  author =	{Dokka, Trivikram and Zemkoho, Alain and Gupta, Sonali Sen and Nobibon, Fabrice Talla},
  title =	{{Pricing Toll Roads under Uncertainty}},
  booktitle =	{16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)},
  pages =	{4:1--4:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-021-7},
  ISSN =	{2190-6807},
  year =	{2016},
  volume =	{54},
  editor =	{Goerigk, Marc and Werneck, Renato F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2016.4},
  URN =		{urn:nbn:de:0030-drops-65289},
  doi =		{10.4230/OASIcs.ATMOS.2016.4},
  annote =	{Keywords: Conditional value at risk, robust optimization, toll pricing}
}
  • Refine by Type
  • 3 Document/PDF
  • 1 Document/HTML

  • Refine by Publication Year
  • 1 2025
  • 1 2017
  • 1 2016

  • Refine by Author
  • 2 Dokka, Trivikram
  • 1 Bhaskar, Umang
  • 1 Eickhoff, Katharina
  • 1 Goerigk, Marc
  • 1 Gupta, Sonali Sen
  • Show More...

  • Refine by Series/Journal
  • 1 LIPIcs
  • 2 OASIcs

  • Refine by Classification
  • 1 Theory of computation → Approximation algorithms analysis
  • 1 Theory of computation → Graph algorithms analysis

  • Refine by Keyword
  • 1 Approximation Algorithms
  • 1 Conditional value at risk
  • 1 Flows over Time
  • 1 Min-Max Disjoint Paths
  • 1 Scheduling
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact