Metric Bases for Polyhedral Gauges

  • Fabien Rebatel
  • Édouard Thiel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)

Abstract

Let (W,d) be a metric space. A subset S ⊆ W is a resolving set for W if d(x,p) = d(y,p) for all p ∈ S implies x = y. A metric basis is a resolving set of minimal cardinality, named the metric dimension (of W). Metric bases and dimensions have been extensively studied for graphs with the intrinsic distance, as well as in the digital plane with the city-block and chessboard distances. We investigate these concepts for polyhedral gauges, which generalize in the Euclidean space the chamfer norms in the digital space.

Keywords

metric basis metric dimension resolving set polyhedral gauge chamfer norms discrete distance distance geometry 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Fabien Rebatel
    • 1
  • Édouard Thiel
    • 1
  1. 1.Laboratoire d’Informatique Fondamentale de Marseille (LIF, UMR 6166)Aix-Marseille UniversitéMarseille cedex 9France

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