Epsilon-covering is NP-complete

Dominique Attali (1) , Tuong-Bach Nguyen (1) , Isabelle Sivignon (1)

1 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes

Consider the dilation and erosion of a shape S by a ball of radius ε. We call ε-covering of S any collection of balls whose union lies between the dilation and erosion of S. We prove that finding an ε-covering of minimum cardinality is NP-complete, using a reduction from vertex cover.

Domaines: Géométrie algorithmique [cs.CG]

Dominique Attali, Tuong-Bach Nguyen, Isabelle Sivignon. Epsilon-covering is NP-complete. EuroCG 2016 - European Workshop on Computational Geometry (EuroCG 2016), Mar 2016, Lugano, Switzerland. ⟨hal-01313158⟩