Abstract
We introduce sphere of influence graphs (SIGs) in the L ∞-metric and study their elementary properties. We argue that SIGs defined with the L ∞-metric are superior to Euclidean SIGs of Toussaint in capturing low-level perceptual information in certain dot patterns. Every graph without isolated vertices is a SIG in the L ∞-metric for all sufficiently high dimensions, and this allows us to define a graphical parameter, the SIG-dimension, that is akin to boxicity. We determine the SIG-dimensions for some classes of graphs and obtain inequalities for others.
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