# MPI-I-92-123

## 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.

Acknowledgement:** **

References to related material:

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

**BibTeX**
`@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},`

`}`