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：针对众多数据处理应用，需要一套全面的优先值管理操作。索引优先队列因其设计特性，在满足这一需求方面尤具潜力。本文报告了一种具备全面操作集的高效索引优先队列的设计与分析。具体而言，$\mathtt{insert}$（插入）、$\mathtt{delete}$（删除）与$\mathtt{decrease}$（减量）操作的时间复杂度期望均为$O(\log^{*}{n})$，而$\mathtt{increase}$（增量）操作通过蒙特卡洛模拟推测其时间复杂度期望为$O(\log\log{n})$。该数据结构的空间复杂度及构建空堆的时间复杂度均为$O(n)$。对于某些大规模计算问题（如超大规模图的分析及（化学）模拟），该堆系统可能展现出显著实用性。