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.
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Rebatel, F., Thiel, É. (2011). Metric Bases for Polyhedral Gauges. In: Debled-Rennesson, I., Domenjoud, E., Kerautret, B., Even, P. (eds) Discrete Geometry for Computer Imagery. DGCI 2011. Lecture Notes in Computer Science, vol 6607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19867-0_10
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