No weak epsilon nets for lines and convex sets in space

Otfried Cheong (1) , Xavier Goaoc (2) , Andreas Holmsen (3)

1 CS - Department of Computer Science [KAIST]
2 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
3 Department of Mathematical Sciences, KAIST

We prove that there exist no weak ε-nets of constant size for lines and convex sets in ℝ^d.

Domaines: Géométrie algorithmique [cs.CG]; Combinatoire [math.CO]

Otfried Cheong, Xavier Goaoc, Andreas Holmsen. No weak epsilon nets for lines and convex sets in space. 2022. ⟨hal-03562077⟩