For many data-processing applications, a comprehensive set of efficient operations for the management of priority values is required. Indexed priority queues are particularly promising to satisfy this requirement by design. In this work, we report the design and analysis of an efficient indexed priority queue with a comprehensive set of operations. In particular, $\mathtt{insert}$, $\mathtt{delete}$ and $\mathtt{decrease}$ all run in expected $O(\log^{*}{n})$ time, while $\mathtt{increase}$ is conjectured by means of Monte Carlo simulations to run in expected $O(\log\log{n})$ time. The space complexity as well as the time complexity for the construction of the empty heap data structure is $O(n)$. For certain massive computational problems, such as specific analyses of extremely large graphs and (chemical) simulations, this heap system may exhibit considerable utility.

翻译：对于许多数据处理应用，需要一套全面的优先级值管理操作。索引优先队列因其设计特性尤其能满足这一需求。本文报告了一种具有全面操作集的高效索引优先队列的设计与分析。特别地，$\mathtt{insert}$（插入）、$\mathtt{delete}$（删除）和$\mathtt{decrease}$（减小）操作均能在期望$O(\log^{*}{n})$时间内完成，而$\mathtt{increase}$（增大）操作经蒙特卡洛模拟推测可在期望$O(\log\log{n})$时间内运行。该空堆数据结构的空间复杂度及构建时间复杂度均为$O(n)$。对于某些大规模计算问题，例如超大规模图的特定分析与（化学）模拟，该堆系统可能展现出显著的实用性。