Geometric set cover problem

The geometric set cover problem is the special case of the set cover problem in geometric settings. The input is a range space Σ = ( X , R ) {\displaystyle \Sigma =(X,{\mathcal {R}})} where X {\displaystyle X} is a universe of points in R d {\displaystyle \mathbb {R} ^{d}} and R {\displaystyle {\mathcal {R}}} is a family of subsets of X {\displaystyle X} called ranges, defined by the intersection of X {\displaystyle X} and geometric shapes such as disks and axis-parallel rectangles.

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