Exact and approximation algorithms for minimum-width cylindrical shells

Pankaj K. Agarwal; Boris Aronov; Micha Sharir

Exact and approximation algorithms for minimum-width cylindrical shells

Pankaj K. Agarwal^*, Boris Aronov, Micha Sharir

^*Corresponding author for this work

Duke University

Research output: Contribution to conference › Paper › peer-review

2 Scopus citations

Abstract

Let S be a set of n points in R³. Let ω* = ω*(S) be the width (i.e., thickness) of a minimum-width infinite cylindrical shell (the region between two co-axial cylinders) containing S. We first present an O(n⁵)-time algorithm for computing ω*, which as far as we know is the first nontrivial algorithm for this problem. We then present an O(n^2+δ)-time algorithm, for any δ>0, that computes a cylindrical shell of width at most 26(1+1/n^4/9)ω* containing S.

Original language	English
Pages	510-517
Number of pages	8
State	Published - 2000
Externally published	Yes
Event	11th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, USA Duration: 9 Jan 2000 → 11 Jan 2000

Conference

Conference	11th Annual ACM-SIAM Symposium on Discrete Algorithms
City	San Francisco, CA, USA
Period	9/01/00 → 11/01/00

Cite this

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title = "Exact and approximation algorithms for minimum-width cylindrical shells",

abstract = "Let S be a set of n points in R3. Let ω* = ω*(S) be the width (i.e., thickness) of a minimum-width infinite cylindrical shell (the region between two co-axial cylinders) containing S. We first present an O(n5)-time algorithm for computing ω*, which as far as we know is the first nontrivial algorithm for this problem. We then present an O(n2+δ)-time algorithm, for any δ>0, that computes a cylindrical shell of width at most 26(1+1/n4/9)ω* containing S.",

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T1 - Exact and approximation algorithms for minimum-width cylindrical shells

AU - Agarwal, Pankaj K.

AU - Aronov, Boris

AU - Sharir, Micha

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N2 - Let S be a set of n points in R3. Let ω* = ω*(S) be the width (i.e., thickness) of a minimum-width infinite cylindrical shell (the region between two co-axial cylinders) containing S. We first present an O(n5)-time algorithm for computing ω*, which as far as we know is the first nontrivial algorithm for this problem. We then present an O(n2+δ)-time algorithm, for any δ>0, that computes a cylindrical shell of width at most 26(1+1/n4/9)ω* containing S.

AB - Let S be a set of n points in R3. Let ω* = ω*(S) be the width (i.e., thickness) of a minimum-width infinite cylindrical shell (the region between two co-axial cylinders) containing S. We first present an O(n5)-time algorithm for computing ω*, which as far as we know is the first nontrivial algorithm for this problem. We then present an O(n2+δ)-time algorithm, for any δ>0, that computes a cylindrical shell of width at most 26(1+1/n4/9)ω* containing S.

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SP - 510

EP - 517

T2 - 11th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 9 January 2000 through 11 January 2000

ER -

Exact and approximation algorithms for minimum-width cylindrical shells

Abstract

Conference

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