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The largest hyper-rectangle in a three dimensional orthogonal polyhedron

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

MPI-I-92-123. June 1992, 7 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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.
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  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},