Online Search for a Hyperplane in High-Dimensional Euclidean Space

Antonios Antoniadis; Ruben Hoeksma; Sándor Kisfaludi-Bak; Kevin Schewior

Online Search for a Hyperplane in High-Dimensional Euclidean Space

Antonios Antoniadis, Ruben Hoeksma, Sándor Kisfaludi-Bak, Kevin Schewior

Research output: Working paper

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Abstract

We consider the online search problem in which a server starting at the origin of a $d$-dimensional Euclidean space has to find an arbitrary hyperplane. The best-possible competitive ratio and the length of the shortest curve from which each point on the $d$-dimensional unit sphere can be seen are within a constant factor of each other. We show that this length is in $\Omega(d)\cap O(d^{3/2})$.

Original language	English
Publisher	arXiv.org
Publication status	Published - 9 Sep 2021

Keywords

cs.CG
cs.DS

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2109.04340v1Submitted version, 1.35 MB

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title = "Online Search for a Hyperplane in High-Dimensional Euclidean Space",

abstract = " We consider the online search problem in which a server starting at the origin of a $d$-dimensional Euclidean space has to find an arbitrary hyperplane. The best-possible competitive ratio and the length of the shortest curve from which each point on the $d$-dimensional unit sphere can be seen are within a constant factor of each other. We show that this length is in $\Omega(d)\cap O(d^{3/2})$. ",

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T1 - Online Search for a Hyperplane in High-Dimensional Euclidean Space

AU - Antoniadis, Antonios

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AU - Kisfaludi-Bak, Sándor

AU - Schewior, Kevin

N1 - Pages: 7, Figures: 2

PY - 2021/9/9

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N2 - We consider the online search problem in which a server starting at the origin of a $d$-dimensional Euclidean space has to find an arbitrary hyperplane. The best-possible competitive ratio and the length of the shortest curve from which each point on the $d$-dimensional unit sphere can be seen are within a constant factor of each other. We show that this length is in $\Omega(d)\cap O(d^{3/2})$.

AB - We consider the online search problem in which a server starting at the origin of a $d$-dimensional Euclidean space has to find an arbitrary hyperplane. The best-possible competitive ratio and the length of the shortest curve from which each point on the $d$-dimensional unit sphere can be seen are within a constant factor of each other. We show that this length is in $\Omega(d)\cap O(d^{3/2})$.

KW - cs.CG

KW - cs.DS

M3 - Working paper

BT - Online Search for a Hyperplane in High-Dimensional Euclidean Space

PB - arXiv.org

ER -

Online Search for a Hyperplane in High-Dimensional Euclidean Space

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Keywords

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