AI 中文总结
本文提出同步堆（sync heap）数据结构，将堆的删除操作与被删元素身份揭示解耦，在用户有限次检查堆状态时实现插入和删除的常数摊还时间，将单位时间调度问题复杂度从O(n log n)优化至最优O(n)。
AI 中文摘要
堆（优先队列）是计算机科学中研究最深入的数据结构之一。本文我们批判性地重新审视教科书假设：在比较模型中，堆的两个标准操作——插入元素和删除最小值——中至少有一个必须花费对数时间。通过将删除操作本身与向用户揭示被删除元素身份的行为解耦，我们避开了排序障碍，在堆操作的复杂度之间获得了一种新的权衡。这表明对数障碍并非删除最小值的固有成本，而是立即获知被删除元素的信息成本。在用户仅有限次检查堆状态的特殊情况下，我们证明插入和删除操作均可支持常数摊还时间。作为应用，这将经典单位时间调度问题的运行时间从O(n log n)改进至最优的O(n)。我们通过设计一种新的数据结构——同步堆（sync heap）来获得上述结果，该结构通过重新排列和压缩自身操作，直到查询迫使其同步并揭示状态来提升速度。作为关键组件，我们使用了Chazelle在其最小生成树算法中引入的软堆（soft heap）。我们的数据结构是简单的、基于比较的确定性结构，且我们的结果具有渐近最优性。
英文摘要
Heaps (priority queues) are among the best-studied data structures in computer science. In this paper, we critically revisit the textbook assumption that in the comparison model at least one of the two standard heap operations of inserting an element and deleting the minimum must take logarithmic time. By decoupling the deletion itself from the act of revealing the identity of the deleted element to the user, we avoid the sorting barrier and obtain a novel trade-off between the complexities of heap operations. This shows that the logarithmic barrier is not inherently the cost of deleting the minimum but rather the information cost of immediately learning which element was deleted. In the special case when the user inspects the heap state only constantly many times, we show that both insertions and deletions can be supported in constant amortized time. As an application, this yields a runtime improvement from $\mathcal{O}(n \log n)$ to the optimal $\mathcal{O}(n)$ for a textbook unit-time scheduling problem. We obtain our results by designing a new data structure, the sync heap, which gains speed by rearranging and compacting its operations until queries force it to synchronize and reveal its state. As a key component, we use the soft heap introduced by Chazelle as part of his minimum spanning tree algorithm. Our data structure is simple, comparison-based, and deterministic, and our results are asymptotically optimal.
