On overlays and minimization diagrams

Vladlen Koltun, Micha Sharir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The overlay of 2 ≤ m ≤ d minimization diagrams of n surfaces in ℝd is isomorphic to a substructure of a suitably constructed minimization diagram of mn surfaces in ℝd+m-1, This elementary observation leads to a new bound on the complexity of the overlay of minimization diagrams of collections of d-variate semi-algebraic surfaces, a tight bound on the complexity of the overlay of minimization diagrams of collections of hyperplanes, and faster algorithms for constructing such overlays. Further algorithmic implications are discussed.

Original languageEnglish
Title of host publicationProceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06
PublisherAssociation for Computing Machinery (ACM)
Pages395-401
Number of pages7
ISBN (Print)1595933409, 9781595933409
DOIs
StatePublished - 2006
Event22nd Annual Symposium on Computational Geometry 2006, SCG'06 - Sedona, AZ, United States
Duration: 5 Jun 20067 Jun 2006

Publication series

NameProceedings of the Annual Symposium on Computational Geometry
Volume2006

Conference

Conference22nd Annual Symposium on Computational Geometry 2006, SCG'06
Country/TerritoryUnited States
CitySedona, AZ
Period5/06/067/06/06

Keywords

  • Arrangements
  • Hyperplanes
  • Lower envelopes
  • Minimization diagrams
  • Overlays
  • Power diagrams
  • Voronoi diagrams

Fingerprint

Dive into the research topics of 'On overlays and minimization diagrams'. Together they form a unique fingerprint.

Cite this