Sphere of influence graphs and the L∞-metric

Authors:
T. S. Michael;Thomas Quint
Affiliations:
Mathematics Department, United States Naval Academy, Annapolis, MD;Department of Mathematics, University of Nevada, Reno, NV
Venue:
Discrete Applied Mathematics
Year:
2003

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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.