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MPI-INF/SWS Research Reports 1991-2021

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MPI-I-92-123

The largest hyper-rectangle in a three dimensional orthogonal polyhedron

Krithivasan, Kamala and Vanisree, R. and Datta, Amitava

June 1992, 7 pages.

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Status: available - back from printing

Given a three dimensional orthogonal polyhedron P, we present a simple and efficient algorithm for finding the three dimensional orthogonal hyper-rectangle R of maximum volume, such that R is completely contained in P. Our algorithm finds out the three dimensional hyper-rectangle of maximum volume by using space sweep technique and enumerating all possible such rectangles. The presented algorithm runs in O(($n^2$+K)logn) time using O(n) space, where n is the number of vertices of the given polyhedron P and K is the number of reported three dimensional orthogonal hyper-rectangles for a problem instance, which is O($n^3$) in the worst case.

URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1992-123

Hide details for BibTeXBibTeX
@TECHREPORT{KrithivasanVanisreeDatta92,
  AUTHOR = {Krithivasan, Kamala and Vanisree, R. and Datta, Amitava},
  TITLE = {The largest hyper-rectangle in a three dimensional orthogonal polyhedron},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-92-123},
  MONTH = {June},
  YEAR = {1992},
  ISSN = {0946-011X},
}