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The largest hyper-rectangle in a three dimensional orthogonal polyhedron

MPS-Authors

Krithivasan,  Kamala
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Vanisree,  R.
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Datta,  Amitava
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-92-123.pdf
(Any fulltext), 12MB

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Citation

Krithivasan, K., Vanisree, R., & Datta, A.(1992). The largest hyper-rectangle in a three dimensional orthogonal polyhedron (MPI-I-92-123). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B6F9-4
Abstract
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.