Metric bases for polyhedral gauges

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. © 2011 Springer-Verlag.