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A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels

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Computer Science – Theory and Applications (CSR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12159))

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Abstract

We prove a \(\varOmega (\sqrt{n})\) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular it is planar and has bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 83% of an upper bound given by a constructed CH.

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Notes

  1. 1.

    We define hop length as the number of nodes here.

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Authors and Affiliations

  1. Institut für Formale Methoden der Informatik, Universität Stuttgart, Stuttgart, Germany

    Tobias Rupp & Stefan Funke

Authors
  1. Tobias Rupp
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  2. Stefan Funke
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Correspondence to Tobias Rupp .

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Editors and Affiliations

  1. University of Trier, Trier, Germany

    Henning Fernau

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Rupp, T., Funke, S. (2020). A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels. In: Fernau, H. (eds) Computer Science – Theory and Applications. CSR 2020. Lecture Notes in Computer Science(), vol 12159. Springer, Cham. https://doi.org/10.1007/978-3-030-50026-9_26

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  • DOI: https://doi.org/10.1007/978-3-030-50026-9_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-50025-2

  • Online ISBN: 978-3-030-50026-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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