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The Number of Bits Needed to Represent a Unit Disk Graph

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Graph Theoretic Concepts in Computer Science (WG 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6410))

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Abstract

We prove that for sufficiently large n, there exist unit disk graphs on n vertices such that for every representation with disks in the plane at least \(c^{\sqrt{n}}\) bits are needed to write down the coordinates of the centers of the disks, for some c> 1. We also show that d n bits always suffice, for some d>1.

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McDiarmid, C., Müller, T. (2010). The Number of Bits Needed to Represent a Unit Disk Graph. In: Thilikos, D.M. (eds) Graph Theoretic Concepts in Computer Science. WG 2010. Lecture Notes in Computer Science, vol 6410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16926-7_29

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  • DOI: https://doi.org/10.1007/978-3-642-16926-7_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16925-0

  • Online ISBN: 978-3-642-16926-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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