2 Search Results for "Casas, Pedro M."

Document
DOI: 10.4230/OASIcs.ATMOS.2021.7
Optimal Forks: Preprocessing Single-Source Shortest Path Instances with Interval Data

Authors: Niels Lindner, Pedro Maristany de las Casas, and Philine Schiewe

Published in: OASIcs, Volume 96, 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)

Abstract
We investigate preprocessing for single-source shortest path queries in digraphs, where arc costs are only known to lie in an interval. More precisely, we want to decide for each arc whether it is part of some shortest path tree for some realization of costs. We show that this problem is solvable in polynomial time by giving a combinatorial algorithm, using optimal structures that we call forks. Our algorithm turns out to be very efficient in practice, and is sometimes even superior in quality to a heuristic developed for the one-to-one shortest path problem in the context of passenger routing in public transport.
Cite as

Niels Lindner, Pedro Maristany de las Casas, and Philine Schiewe. Optimal Forks: Preprocessing Single-Source Shortest Path Instances with Interval Data. In 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021). Open Access Series in Informatics (OASIcs), Volume 96, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{lindner_et_al:OASIcs.ATMOS.2021.7,
  author =	{Lindner, Niels and Maristany de las Casas, Pedro and Schiewe, Philine},
  title =	{{Optimal Forks: Preprocessing Single-Source Shortest Path Instances with Interval Data}},
  booktitle =	{21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)},
  pages =	{7:1--7:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-213-6},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{96},
  editor =	{M\"{u}ller-Hannemann, Matthias and Perea, Federico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2021.7},
  URN =		{urn:nbn:de:0030-drops-148767},
  doi =		{10.4230/OASIcs.ATMOS.2021.7},
  annote =	{Keywords: Preprocessing Shortest Path Problems, Interval Data, Graph Algorithms}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2017.15
Cost Projection Methods for the Shortest Path Problem with Crossing Costs

Authors: Marco Blanco, Ralf Borndörfer, Nam Dung Hoàng, Anton Kaier, Pedro M. Casas, Thomas Schlechte, and Swen Schlobach

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

Abstract
Real world routing problems, e.g., in the airline industry or in public and rail transit, can feature complex non-linear cost functions. An important case are costs for crossing regions, such as countries or fare zones. We introduce the shortest path problem with crossing costs (SPPCC) to address such situations; it generalizes the classical shortest path problem and variants such as the resource constrained shortest path problem and the minimum label path problem. Motivated by an application in flight trajectory optimization with overflight costs, we focus on the case in which the crossing costs of a region depend only on the nodes used to enter or exit it. We propose an exact Two-Layer-Dijkstra Algorithm as well as a novel cost-projection linearization technique that transforms crossing costs into shadow costs on individual arcs, thus approximating the SPPCC by a standard shortest path problem. We evaluate all algorithms' performance on real-world flight trajectory optimization instances, obtaining very good à posteriori error bounds.
Cite as

Marco Blanco, Ralf Borndörfer, Nam Dung Hoàng, Anton Kaier, Pedro M. Casas, Thomas Schlechte, and Swen Schlobach. Cost Projection Methods for the Shortest Path Problem with Crossing Costs. In 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017). Open Access Series in Informatics (OASIcs), Volume 59, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{blanco_et_al:OASIcs.ATMOS.2017.15,
  author =	{Blanco, Marco and Bornd\"{o}rfer, Ralf and Dung Ho\`{a}ng, Nam and Kaier, Anton and Casas, Pedro M. and Schlechte, Thomas and Schlobach, Swen},
  title =	{{Cost Projection Methods for the Shortest Path Problem with Crossing Costs}},
  booktitle =	{17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)},
  pages =	{15:1--15:14},
  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-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2017.15},
  URN =		{urn:nbn:de:0030-drops-78939},
  doi =		{10.4230/OASIcs.ATMOS.2017.15},
  annote =	{Keywords: shortest path problem, resource constrained shortest path, crossing costs, flight trajectory optimization, overflight fees, cost projection}
}
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