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 $\Omega(d)\cap O(d^{3/2})$.

翻译：我们考虑了在线搜索问题,即一个服务器从美元维度的欧几里德空间的源头开始,必须找到一个任意的超高飞机。最有可能的竞争性比率和最短曲线的长度,从中可以看到美元维度单位域的每个点,都是在一个不变的系数之内。我们显示,这一长度是$\Omega(d)\ cap O(d ⁇ 3/2}美元。