Suppose we are searching for a target point t in a certain restricted search space. To pinpoint the location of t, we issue query points $q_1,\dots ,q_n$ in the search space. As a response, we obtain an ordering of the query points by distance to t. This restricts possible locations of t. In this paper, we consider the case where the search space is the unit interval $[0,1]$. We define the accuracy of a query strategy as the reciprocal of the size of the subinterval to which we can pinpoint t in the worst case. We describe a strategy with accuracy $\mathrm{\Theta }(n^2)$, which is at most a factor two from optimal if all query points have to be generated at once. With query points generated one by one depending on the response received on previous query points, we achieve accuracy $\mathrm{\Omega }({2.29}^n)$, and prove that no strategy can achieve $\mathrm{\Omega }({3.66}^n)$. These strategies can be extended to higher dimensional cases, where the search space is the unit cube or unit ball.

假设我们正在某个受限搜索空间中搜索目标点t。为了查明t的位置，我们发出查询点$q_{\mathrm{1个}}，\dots ，q_{ñ}$在搜索空间中。作为响应，我们按距t的距离获得查询点的顺序。这限制了t的可能位置。在本文中，我们考虑搜索空间为单位间隔的情况$[0，\mathrm{1个}]$。我们定义的准确性查询战略，这是我们能够查明子区间的长度的倒数ŧ在最坏的情况下。我们准确描述策略$\mathrm{\Theta }（{ñ}^2）$，如果必须一次生成所有查询点，则最多是优化的两倍。通过根据先前查询点收到的响应一个一生成一个查询点，我们达到了准确性$\mathrm{\Omega }（{2.29}^{ñ}）$，并证明没有策略可以实现 $\mathrm{\Omega }（{3.66}^{ñ}）$。这些策略可以扩展到更高维度的情况，其中搜索空间是单位立方体或单位球。