AI 中文总结
研究提出纯配对堆，通过消除删除最小元素操作中的合并步骤简化配对堆。给出其操作的摊还时间界，与多遍配对堆匹配，除减小键值界外也与自调整堆下界相符。分析方法是分组分析，该方法也适用于惰性配对堆。
AI 中文摘要
配对堆是堆（优先队列）的一种“自调整”实现，因其简单高效而在实践中广泛使用。我们引入并分析了一种简化版的配对堆，即纯配对堆。我们的创新在于消除了删除最小元素操作中的合并步骤。对于纯配对堆的操作，我们得到了如下摊还时间界：每次删除最小元素为\(O(\log n)\)时间，每次减小键值操作是\(O(\log\log n \cdot \log\log\log n)\)时间，每次插入或合并为\(O(1)\)时间。这些界与最近为更复杂的多遍配对堆得到的界相匹配，除减小键值界外，它们也与自调整堆的已知下界匹配，该界在已知下界的\(\log\log\log n\)因子范围内。我们分析的主要新颖之处在于将堆元素分组并分别分析每组。我们的分析扩展后可为惰性配对堆（配对堆的多树版本）给出相同的界。
英文摘要
The pairing heap is a "self-adjusting" implementation of a heap (priority queue) that is widely used in practice because it is simple and efficient. We introduce and analyze a simplified version of the pairing heap that we call the pure pairing heap. Our innovation is to eliminate the assembly pass during delete-min operations. We obtain the following amortized time bounds for operations on pure pairing heaps: $O(\log n)$ time per delete-min, $O(\log\log n \cdot \log\log\log n)$ time per decrease-key operation, and $O(1)$ time for each insert or meld. These bounds match those recently obtained for a more complicated version of pairing heaps, the multipass pairing heap}. These bounds also match the known lower bounds for self-adjusting heaps, except for the decrease-key bound, which is within a factor of $\log\log\log n$ of the lower bound. The main novelty in our analysis is to partition heap items into groups and to analyze each group separately. Our analysis extends to give the same bounds for lazy pairing heaps, a multitree version of pairing heaps.
