Skip to Main content Skip to Navigation

Helly-type theorems for approximate covering

Julien Demouth 1 Olivier Devillers 2 Marc Glisse 1 Xavier Goaoc 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 GEOMETRICA - Geometric computing
INRIA Futurs, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Let F be a covering of a unit ball U in Rd by unit balls. We prove that for any epsilon >0, the smallest subset of F leaving at most a volume epsilon of U uncovered has size O(epsilon^((1-d)/2)polylog 1/epsilon). We give an example showing that this bound is tight in the worst-case, up to a logarithmic factor, and deduce an algorithm to compute such a small subset of F. We then extend these results in several directions, including covering boxes by boxes and visibility among disjoint unit balls in R3.
Document type :
Complete list of metadata

Cited literature [12 references]  Display  Hide  Download
Contributor : Olivier Devillers Connect in order to contact the contributor
Submitted on : Monday, November 5, 2007 - 1:20:25 PM
Last modification on : Friday, January 21, 2022 - 3:10:58 AM
Long-term archiving on: : Friday, November 25, 2016 - 7:13:01 PM


Files produced by the author(s)


  • HAL Id : inria-00179277, version 3



Julien Demouth, Olivier Devillers, Marc Glisse, Xavier Goaoc. Helly-type theorems for approximate covering. [Research Report] RR-6342, INRIA. 2007, pp.12. ⟨inria-00179277v3⟩



Les métriques sont temporairement indisponibles