We study the median slope selection problem in the oblivious RAM model. In this model memory accesses have to be independent of the data processed, i.e., an adversary cannot use observed access patterns to derive additional information about the input. We show how to modify the randomized algorithm of Matou\v{s}ek (1991) to obtain an oblivious version with $\mathcal{O}(n \log^2 n)$ expected time for $n$ points in $\mathbb{R}^2$. This complexity matches a theoretical upper bound that can be obtained through general oblivious transformation. In addition, results from a proof-of-concept implementation show that our algorithm is also practically efficient.

翻译：我们研究在遗忘RAM模型中的中位数斜率选择问题。在此模型中，内存访问必须与处理的数据无关，即敌手无法通过观察访问模式来推导输入的额外信息。我们展示了如何修改Matoušek（1991）的随机化算法，以获得一个遗忘版本，该版本对于$\mathbb{R}^2$中的$n$个点具有$\mathcal{O}(n \log^2 n)$的期望运行时间。这一复杂度与通过通用遗忘变换可获得的理论上界相匹配。此外，概念验证实现的结果表明，我们的算法在实际中也是高效的。