Online Search for a Hyperplane in High-Dimensional Euclidean Space

09/09/2021

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by   Antonios Antoniadis, et al.

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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)∩ O(d^3/2).