Improved Bounds for Wireless Localization

  • Tobias Christ
  • Michael Hoffmann
  • Yoshio Okamoto
  • Takeaki Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5124)

Abstract

We consider a novel class of art gallery problems inspired by wireless localization. Given a simple polygon P, place and orient guards each of which broadcasts a unique key within a fixed angular range. Broadcasts are not blocked by the edges of P. The interior of the polygon must be described by a monotone Boolean formula composed from the keys. We improve both upper and lower bounds for the general setting by showing that the maximum number of guards to describe any simple polygon on n vertices is between roughly \({\frac{3}{5}}\)n and \(\frac{4}{5}\)n. For the natural setting where guards may be placed aligned to one edge or two consecutive edges of P only, we prove that n − 2 guards are always sufficient and sometimes necessary.

Keywords

Convex Hull Simple Polygon Extremal Vertex Polygonal Chain Improve Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Tobias Christ
    • 1
  • Michael Hoffmann
    • 1
  • Yoshio Okamoto
    • 2
  • Takeaki Uno
    • 3
  1. 1.Institute for Theoretical Computer ScienceETH ZürichSwitzerland
  2. 2.Tokyo Institute of TechnologyJapan
  3. 3.National Institute of InformaticsTokyoJapan

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