Covering a set of points by two axis-parallel boxes

Sergei Bespamyatnikh; Michael Segal

doi:10.1016/S0020-0190(00)00093-4

Covering a set of points by two axis-parallel boxes

Sergei Bespamyatnikh, Michael Segal

School of Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

An efficient algorithm is presented for solving the min-max two-box problem in arbitrary dimension d≥2. The runtime of the algorithm is O(n log n+n^d-1). For the plane, the algorithm is simpler than that of Glozman et al. since the only data structure used in the algorithm is a list and it runs in O(n) time after O(n log n) presorting step. The efficiency of the algorithm is based on the monotonicity of the evaluated function in the problem.

Original language	English
Pages (from-to)	95-100
Number of pages	6
Journal	Information Processing Letters
Volume	75
Issue number	3
DOIs	https://doi.org/10.1016/S0020-0190(00)00093-4
State	Published - 31 Aug 2000

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/S0020-0190(00)00093-4

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title = "Covering a set of points by two axis-parallel boxes",

abstract = "An efficient algorithm is presented for solving the min-max two-box problem in arbitrary dimension d≥2. The runtime of the algorithm is O(n log n+nd-1). For the plane, the algorithm is simpler than that of Glozman et al. since the only data structure used in the algorithm is a list and it runs in O(n) time after O(n log n) presorting step. The efficiency of the algorithm is based on the monotonicity of the evaluated function in the problem.",

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N2 - An efficient algorithm is presented for solving the min-max two-box problem in arbitrary dimension d≥2. The runtime of the algorithm is O(n log n+nd-1). For the plane, the algorithm is simpler than that of Glozman et al. since the only data structure used in the algorithm is a list and it runs in O(n) time after O(n log n) presorting step. The efficiency of the algorithm is based on the monotonicity of the evaluated function in the problem.

AB - An efficient algorithm is presented for solving the min-max two-box problem in arbitrary dimension d≥2. The runtime of the algorithm is O(n log n+nd-1). For the plane, the algorithm is simpler than that of Glozman et al. since the only data structure used in the algorithm is a list and it runs in O(n) time after O(n log n) presorting step. The efficiency of the algorithm is based on the monotonicity of the evaluated function in the problem.

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Covering a set of points by two axis-parallel boxes

Abstract

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