We give a (strongly) history-independent two-choice balls-and-bins algorithm on $n$ bins that supports both insertions and deletions on a set of up to $m$ balls, while guaranteeing a maximum load of $m / n + O(1)$ with high probability, and achieving an expected recourse of $O(\log \log (m/n))$ per operation. To the best of our knowledge, this is the first history-independent solution to achieve nontrivial guarantees of any sort for $m/n \ge ω(1)$ and is the first fully dynamic solution (history independent or not) to achieve $O(1)$ overload with $o(m/n)$ expected recourse.

翻译：我们提出了一种（强）历史无关的双选择球与箱算法，该算法在 $n$ 个箱子上支持对最多 $m$ 个球的集合进行插入和删除操作，同时以高概率保证最大负载为 $m / n + O(1)$，并实现每次操作 $O(\log \log (m/n))$ 的期望调整开销。据我们所知，这是首个在 $m/n \ge ω(1)$ 时实现任何非平凡保证的历史无关解决方案，也是首个（无论是否历史无关）实现 $O(1)$ 过载且期望调整开销为 $o(m/n)$ 的完全动态解决方案。