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Scandinavian Workshop on Algorithm Theory

SWAT 2006: Algorithm Theory – SWAT 2006 pp 388–399Cite as

On Spanners of Geometric Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4059))

Abstract

Given a connected geometric graph G, we consider the problem of constructing a t-spanner of G having the minimum number of edges. We prove that for every t with \(1 < t < \frac{1}{4} \log n\), there exists a connected geometric graph G with n vertices, such that every t-spanner of G contains Ω( n 1 + 1/t ) edges. This bound almost matches the known upper bound, which states that every connected weighted graph with n vertices contains a t-spanner with O(tn 1 + 2/(t + 1)) edges. We also prove that the problem of deciding whether a given geometric graph contains a t-spanner with at most K edges is NP-hard. Previously, this NP-hardness result was only known for non-geometric graphs.

JG was funded by the Australian Government’s Backing Australia’s Ability initiative, in part through the Australian Research Council. MS was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Part of this work was done while MS visited NICTA.

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Author information

Authors and Affiliations

  1. National ICT Australia Ltd., Sydney, Australia

    Joachim Gudmundsson

  2. School of Computer Science, Carleton University, Ottawa, Ontario, Canada

    Michiel Smid

Authors
  1. Joachim Gudmundsson
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  2. Michiel Smid
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Editor information

Editors and Affiliations

  1. MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Lars Arge

  2. Institute of Mathematics and Computer Science, University of Latvia, Raiņa bulvāris 29, Rīga, LV-1459, Latvia

    Rusins Freivalds

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© 2006 Springer-Verlag Berlin Heidelberg

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Gudmundsson, J., Smid, M. (2006). On Spanners of Geometric Graphs. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_36

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  • DOI: https://doi.org/10.1007/11785293_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35753-7

  • Online ISBN: 978-3-540-35755-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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