A large group of data-processing applications often require a comprehensive set of efficient operations for priority value management. Indexed priority queues are particularly useful in this context. 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 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 system are $O(n)$. For massive computational problems, such as (chemical) simulations or the specific analyses of very large graphs, the heap data structure is expected to exhibit utility.

翻译：大量数据处理应用通常需要一套全面的高效操作来管理优先权值。在此背景下，索引优先队列尤为实用。本文报告了一种具备全面操作集合的高效索引优先队列的设计与分析。具体而言，$\mathtt{insert}$、$\mathtt{delete}$ 和 $\mathtt{decrease}$ 的期望运行时间均为 $O(\log^{*}{n})$，而 $\mathtt{increase}$ 的期望运行时间推测为 $O(\log\log{n})$。空间复杂度以及空堆系统构建的时间复杂度均为 $O(n)$。对于诸如（化学）模拟或超大规模图特定分析等大规模计算问题，该堆数据结构预计将展现出实用价值。