Computing the volume of the union of cubes

Pankaj K. Agarwal*, Haim Kaplan, Micha Sharir

*Corresponding author for this work

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

Abstract

Let C be a set of n axis-aligned cubes in R 3, and let U(C) denote the union of C. We present an algorithmthat can compute the volume of U(C) in time O(n 4/3 log n). The previously best known algorithm, by Overmars and Yap, computes the volume of the union ofany n axis-aligned boxes in R 3 in O(n 3/2log n) time.

Original languageEnglish
Title of host publicationProceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07
Pages294-301
Number of pages8
DOIs
StatePublished - 2007
Event23rd Annual Symposium on Computational Geometry, SCG'07 - Gyeongju, Korea, Republic of
Duration: 6 Jun 20078 Jun 2007

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Conference

Conference23rd Annual Symposium on Computational Geometry, SCG'07
Country/TerritoryKorea, Republic of
CityGyeongju
Period6/06/078/06/07

Keywords

  • Arrangements
  • Union of objects

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