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Constructing Sparse t-Spanners with Small Separators

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Fundamentals of Computation Theory (FCT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2751))

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Abstract

Given a set of n points \(\mathcal{S}\) in the plane and a real value t>1 we show how to construct in time \(\mathcal{O}(n {\rm log} n)\) a t-spanner \(\mathcal{G}\) of \(\mathcal{S}\) such that there exists a set of vertices \(\mathcal{S'}\) of size \(\mathcal{O}(\sqrt{n} {\rm log} n)\) whose removal leaves two disconnected sets \(\mathcal{A}\) and \(\mathcal{B}\) where neither is of size greater than 2/3 · n. The spanner also has some additional properties; low weight and constant degree.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computing Science, TU Eindhoven, 5600 MB, Eindhoven, The Netherlands

    Joachim Gudmundsson

Authors
  1. Joachim Gudmundsson
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Lund University, 22100, Lund, Sweden

    Andrzej Lingas

  2. School of Technology and Society, Malmö University, SE-205 06, Malmö, Sweden

    Bengt J. Nilsson

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© 2003 Springer-Verlag Berlin Heidelberg

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Gudmundsson, J. (2003). Constructing Sparse t-Spanners with Small Separators. In: Lingas, A., Nilsson, B.J. (eds) Fundamentals of Computation Theory. FCT 2003. Lecture Notes in Computer Science, vol 2751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45077-1_9

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  • DOI: https://doi.org/10.1007/978-3-540-45077-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40543-6

  • Online ISBN: 978-3-540-45077-1

  • eBook Packages: Springer Book Archive

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