细堆与光滑堆的紧性分析
A Tight Analysis of Slim Heaps and Smooth Heaps
摘要：
平滑堆和与之密切相关的瘦堆是最近发明的堆（优先级队列）数据结构的自调整实现。我们分析了这些数据结构的效率。我们获得了每个操作的时间的摊销界限：$O(1)$用于make-heap、insert、find-min和meld; $O(\log\log n)$用于decrease-key; $O(\log n)$用于delete-min和delete，其中$n$是堆中的当前项数。这些界限不仅对平滑和苗条的堆是严格的，而且对Iacono和Özkan的纯堆模型中的任何堆实现都是严格的，旨在捕获所有可能的“自调整”堆实现。苗条和光滑堆是第一个已知的数据结构，以匹配Iacono和Özkan的下限，并满足其模型的约束。我们的分析建立在Pettie对配对堆（一种经典的自调整堆实现）效率的见解之上。
英文摘要：
The smooth heap and the closely related slim heap are recently invented self-adjusting implementations of the heap (priority queue) data structure. We analyze the efficiency of these data structures. We obtain the following amortized bounds on the time per operation: $O(1)$ for make-heap, insert, find-min, and meld; $O(\log\log n)$ for decrease-key; and $O(\log n)$ for delete-min and delete, where $n$ is the current number of items in the heap. These bounds are tight not only for smooth and slim heaps but for any heap implementation in Iacono and Özkan's pure heap model, intended to capture all possible "self-adjusting" heap implementations. Slim and smooth heaps are the first known data structures to match Iacono and Özkan's lower bounds and to satisfy the constraints of their model. Our analysis builds on Pettie's insights into the efficiency of pairing heaps, a classical self-adjusting heap implementation.
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