Online Search for a Hyperplane in High-Dimensional Euclidean Space Article Swipe
Related Concepts
Hyperplane
Point (geometry)
Constant (computer programming)
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Computer science
Geometry
Programming language
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Antonios P. Antoniadis
,
Ruben Hoeksma
,
Sándor Kisfaludi-Bak
,
Kevin Schewior
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2109.04340
· OA: W4286981258
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2109.04340
· OA: W4286981258
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 $Ω(d)\cap O(d^{3/2})$.
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