Combinatorial complexity of translating a box in polyhedral 3-space

Dan Halperin; Chee Keng Yap

doi:10.1145/160985.160992

Combinatorial complexity of translating a box in polyhedral 3-space

Dan Halperin^*, Chee Keng Yap

^*Corresponding author for this work

Stanford University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

We study the space of free translations of a box amidst polyhedral obstacles with n features. We show that the combinatorial complexity of this space is O(n²α(n)) where α(n) is the inverse Ackermann function. Our bound is within an α(n) factor off the lower bound, and it constitutes an improvement of almost an order of magnitude over the best previously known (and naive) bound for this problem, O(n³).

Original language	English
Title of host publication	Proceedings of the 9th Annual Symposium on Computational Geometry
Publisher	Association for Computing Machinery (ACM)
Pages	29-37
Number of pages	9
ISBN (Print)	0897915828, 9780897915823
DOIs	https://doi.org/10.1145/160985.160992
State	Published - 1993
Externally published	Yes
Event	Proceedings of the 9th Annual Symposium on Computational Geometry - San Diego, CA, USA Duration: 19 May 1993 → 21 May 1993

Publication series

Name	Proceedings of the 9th Annual Symposium on Computational Geometry

Conference

Conference	Proceedings of the 9th Annual Symposium on Computational Geometry
City	San Diego, CA, USA
Period	19/05/93 → 21/05/93

Funding

Funders	Funder number
National Science Foundation	9002819

Access to Document

10.1145/160985.160992

Cite this

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title = "Combinatorial complexity of translating a box in polyhedral 3-space",

abstract = "We study the space of free translations of a box amidst polyhedral obstacles with n features. We show that the combinatorial complexity of this space is O(n2α(n)) where α(n) is the inverse Ackermann function. Our bound is within an α(n) factor off the lower bound, and it constitutes an improvement of almost an order of magnitude over the best previously known (and naive) bound for this problem, O(n3).",

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Halperin, D & Yap, CK 1993, Combinatorial complexity of translating a box in polyhedral 3-space. in Proceedings of the 9th Annual Symposium on Computational Geometry. Proceedings of the 9th Annual Symposium on Computational Geometry, Association for Computing Machinery (ACM), pp. 29-37, Proceedings of the 9th Annual Symposium on Computational Geometry, San Diego, CA, USA, 19/05/93. https://doi.org/10.1145/160985.160992

Combinatorial complexity of translating a box in polyhedral 3-space. / Halperin, Dan; Yap, Chee Keng.
Proceedings of the 9th Annual Symposium on Computational Geometry. Association for Computing Machinery (ACM), 1993. p. 29-37 (Proceedings of the 9th Annual Symposium on Computational Geometry).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Combinatorial complexity of translating a box in polyhedral 3-space

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