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VC-Dimension and Shortest Path Algorithms

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Automata, Languages and Programming (ICALP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6755))

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Abstract

We explore the relationship between VC-dimension and graph algorithm design. In particular, we show that set systems induced by sets of vertices on shortest paths have VC-dimension at most two. This allows us to use a result from learning theory to improve time bounds on query algorithms for the point-to-point shortest path problem in networks of low highway dimension, such as road networks. We also refine the definitions of highway dimension and related concepts, making them more general and potentially more relevant to practice. In particular, we define highway dimension in terms of set systems induced by shortest paths, and give cardinality-based and average case definitions.

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Author information

Authors and Affiliations

  1. Microsoft Research Silicon Valley, USA

    Ittai Abraham, Daniel Delling, Andrew V. Goldberg & Renato F. Werneck

  2. Tel Aviv University, Israel

    Amos Fiat

Authors
  1. Ittai Abraham
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  2. Daniel Delling
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  3. Amos Fiat
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  4. Andrew V. Goldberg
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  5. Renato F. Werneck
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Editor information

Editors and Affiliations

  1. ICE-TCS, School of Computer Science, Reykjavik University, Menntavegur 1, IS 101, Reykjavik, Iceland

    Luca Aceto

  2. Fakultät für Informatik, Universität Wien, Universitätsstraße10/9, 1090, Wien, Österreich, Austria

    Monika Henzinger

  3. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Jiří Sgall

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© 2011 Springer-Verlag Berlin Heidelberg

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Abraham, I., Delling, D., Fiat, A., Goldberg, A.V., Werneck, R.F. (2011). VC-Dimension and Shortest Path Algorithms. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22006-7_58

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  • DOI: https://doi.org/10.1007/978-3-642-22006-7_58

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22005-0

  • Online ISBN: 978-3-642-22006-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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