软序列堆
Soft Sequence Heaps
摘要：
Chazelle [JACM 00]介绍了软堆作为有效的最小生成树算法的构建块，最近Kaplan等人[SOSA 2019]展示了如何应用软堆来实现各种选择问题的更简单算法。通过允许在总共$N$插入之后损坏堆中的项目的$εN$，软堆权衡效率的准确性，其中损坏的项目是具有人为增加的键的项目，并且$0 < ε\leq 1/2$是固定的错误参数。Chazelle的软堆是基于二叉树的，并且支持在摊销$O(\lg(1/ε))$时间内的插入和在摊销$O(1)$时间内的提取最小操作。在本文中，我们探讨了软堆的设计空间。本文的主要贡献是一个替代的软堆实现合并排序序列的基础上，与Chazelle的软堆的时间范围相匹配。我们还讨论了Kaplan等人[SICOMP 2013]的软堆的变体，其中我们避免了懒惰地执行插入。它是基于三进制树而不是二进制树，并匹配卡普兰等人的时间界限，即，摊销的$O(1)$插入和摊销的$O(\lg(1/ε))$ extract-min。我们的两种数据结构都只在extract-min操作之后引入损坏，该操作返回被该操作损坏的项集合。
英文摘要：
Chazelle [JACM00] introduced the soft heap as a building block for efficient minimum spanning tree algorithms, and recently Kaplan et al. [SOSA2019] showed how soft heaps can be applied to achieve simpler algorithms for various selection problems. A soft heap trades-off accuracy for efficiency, by allowing $εN$ of the items in a heap to be corrupted after a total of $N$ insertions, where a corrupted item is an item with artificially increased key and $0 < ε\leq 1/2$ is a fixed error parameter. Chazelle's soft heaps are based on binomial trees and support insertions in amortized $O(\lg(1/ε))$ time and extract-min operations in amortized $O(1)$ time. In this paper we explore the design space of soft heaps. The main contribution of this paper is an alternative soft heap implementation based on merging sorted sequences, with time bounds matching those of Chazelle's soft heaps. We also discuss a variation of the soft heap by Kaplan et al. [SICOMP2013], where we avoid performing insertions lazily. It is based on ternary trees instead of binary trees and matches the time bounds of Kaplan et al., i.e. amortized $O(1)$ insertions and amortized $O(\lg(1/ε))$ extract-min. Both our data structures only introduce corruptions after extract-min operations which return the set of items corrupted by the operation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
