For the continuous minimum-membership geometric set cover problem, the paper provides constant-factor approximation algorithms for squares, hypercubes, disks, and convex polygons, and proves NP-hardness for the minimum 1-ply unit square cover.
Computational Geometry 10(2), 77–87 (1998)
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Minimum Membership Geometric Set Cover in the Continuous Setting
For the continuous minimum-membership geometric set cover problem, the paper provides constant-factor approximation algorithms for squares, hypercubes, disks, and convex polygons, and proves NP-hardness for the minimum 1-ply unit square cover.