We study sorting algorithms based on randomized round-robin comparisons. Specifically, we study Spin-the-bottle sort, where comparisons are unrestricted, and Annealing sort, where comparisons are restricted to a distance bounded by a temperature parameter. Both algorithms are simple, randomized, data-oblivious sorting algorithms, which are useful in privacy-preserving computations, but, as we show, Annealing sort is much more efficient. We show that there is an input permutation that causes Spin-the-bottle sort to require Ω(n2logn) expected time in order to succeed, and that in O(n2logn) time this algorithm succeeds with high probability for any input. We also show there is a specification of Annealing sort that runs in O(nlogn) time and succeeds with very high probability.

中文翻译：

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Spin-the-Bottle Sort 和 Annealing Sort：通过循环随机比较进行遗忘排序

我们研究基于随机循环比较的排序算法。具体来说，我们研究了旋转瓶排序（其中比较不受限制）和退火排序（其中比较仅限于由温度参数限定的距离）。这两种算法都是简单的、随机的、不考虑数据的排序算法，它们在隐私保护计算中很有用，但是，正如我们所展示的，退火排序效率更高。我们表明，有一个输入排列导致旋转瓶排序需要 Ω(n2logn) 预期时间才能成功，并且在 O(n2logn) 时间内，该算法对任何输入都有很高的概率成功。我们还展示了在 O(nlogn) 时间内运行并以非常高的概率成功的退火排序规范。