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DOI: 10.4230/LIPIcs.ESA.2022.14

An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions

Authors: Florian Barth, Stefan Funke, and Claudius Proissl

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

Abstract

Graphs with multiple edge costs arise naturally in the route planning domain when apart from travel time other criteria like fuel consumption or positive height difference are also objectives to be minimized. In such a scenario, this paper investigates the number of extreme shortest paths between a given source-target pair s, t. We show that for a fixed but arbitrary number of cost types d ≥ 1 the number of extreme shortest paths is in n^O(log^{d-1}n) in graphs G with n nodes. This is a generalization of known upper bounds for d = 2 and d = 3.

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Florian Barth, Stefan Funke, and Claudius Proissl. An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 14:1-14:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{barth_et_al:LIPIcs.ESA.2022.14,
  author =	{Barth, Florian and Funke, Stefan and Proissl, Claudius},
  title =	{{An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{14:1--14:12},
  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.2022.14},
  URN =		{urn:nbn:de:0030-drops-169525},
  doi =		{10.4230/LIPIcs.ESA.2022.14},
  annote =	{Keywords: Parametric Shortest Paths, Extreme Shortest Paths}
}

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DOI: 10.4230/LIPIcs.ISAAC.2021.15

Preference-Based Trajectory Clustering - An Application of Geometric Hitting Sets

Authors: Florian Barth, Stefan Funke, and Claudius Proissl

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract

In a road network with multicriteria edge costs we consider the problem of computing a minimum number of driving preferences such that a given set of paths/trajectories is optimal under at least one of these preferences. While the exact formulation and solution of this problem appears theoretically hard, we show that in practice one can solve the problem exactly even for non-homeopathic instance sizes of several thousand trajectories in a road network of several million nodes. We also present a parameterized guaranteed-polynomial-time scheme with very good practical performance.

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Florian Barth, Stefan Funke, and Claudius Proissl. Preference-Based Trajectory Clustering - An Application of Geometric Hitting Sets. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{barth_et_al:LIPIcs.ISAAC.2021.15,
  author =	{Barth, Florian and Funke, Stefan and Proissl, Claudius},
  title =	{{Preference-Based Trajectory Clustering - An Application of Geometric Hitting Sets}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{15:1--15:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.15},
  URN =		{urn:nbn:de:0030-drops-154481},
  doi =		{10.4230/LIPIcs.ISAAC.2021.15},
  annote =	{Keywords: Route planning, personalization, computational geometry}
}

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Documents authored by Barth, Florian

An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions

Abstract

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Preference-Based Trajectory Clustering - An Application of Geometric Hitting Sets

Abstract

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