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arXiv · 2109.04340

Online Search for a Hyperplane in High-Dimensional Euclidean Space

Antonios Antoniadis·Ruben Hoeksma·Sándor Kisfaludi-Bak·Kevin Schewior
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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 $\Omega(d)\cap O(d^{3/2})$.

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Antonios Antoniadis, Ruben Hoeksma, Sándor Kisfaludi-Bak, Kevin Schewior. 2021-09-09. Online Search for a Hyperplane in High-Dimensional Euclidean Space. https://arxiv.org/abs/2109.04340

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