共享对象摊销时间复杂度的下限

IF 0.6 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS
Hagit Attiya, Arie Fouren, Jeremy Ko
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引用次数: 0

摘要

实现的摊销步骤复杂度衡量的是整体性能,而不是单个操作的性能。具体来说,实现的摊销步骤复杂度是在最坏情况下,所有可能执行中调用操作执行的平均步骤数。执行的点争用 \(\dot{c}\)表示,衡量的是执行中同时激活的预进程的最大数量。Ruppert (2016)表明,许多共享数据结构的已知无锁实现的摊销步骤复杂度包括一个与点争用(\(\dot{c}\))线性的添加因子。本文表明,在队列、栈或堆的读、写、比较原语(如比较&交换)和 LL/SC 的摊销 RMR 复杂性(其中 n 是系统中进程的总数)方面,不存在具有 \(o(\min\{dot{c}, \sqrt{log\log n}\})摊销 RMR 复杂性的无锁实现。此外,论文还展示了共享链表、跳转列表、搜索树和其他基于指针的数据结构的摊销步骤复杂度的下限((\Omega (\min \{dot{c}, \log \log n\})\) )。这些下限意味着,只要与系统中的进程数量相比,点争用很小(即 \(\dot{c}\in O(\sqrt{log \log n})\)或 \(\dot{c}\in O(\log \log n)\)),与 \(\dot{c}\in O(\log \log n)\)线性相关的附加因子对于这些实现来说是固有的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Lower Bounds on the Amortized Time Complexity of Shared Objects

Lower Bounds on the Amortized Time Complexity of Shared Objects

The amortized step complexity of an implementation measures its performance as a whole, rather than the performance of individual operations. Specifically, the amortized step complexity of an implementation is the average number of steps performed by invoked operations, in the worst case, taken over all possible executions. The point contention of an execution, denoted by \(\dot{c}\), measures the maximal number of precesses simultaneously active in the execution. Ruppert (2016) showed that the amortized step complexity of known lock-free implementations for many shared data structures includes an additive factor linear in the point contention \(\dot{c}\). This paper shows that there is no lock-free implementation with \(o(\min \{\dot{c}, \sqrt{\log \log n}\})\) amortized RMR complexity of queues, stacks or heaps from reads, writes, comparison primitives (such as compare &swap) and LL/SC, where n is the total number of the processes in the system. In addition, the paper shows a \(\Omega (\min \{\dot{c}, \log \log n\})\) lower bound on the amortized step complexity for shared linked lists, skip lists, search trees and other pointer-based data structures. These lower bounds mean that the additive factor linear in \(\dot{c}\) is inherent for these implementations, provided that the point contention is small compared to the number of processes in the system (i.e. \(\dot{c}\in O(\sqrt{\log \log n})\) or \(\dot{c}\in O(\log \log n)\)).

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来源期刊
Theory of Computing Systems
Theory of Computing Systems 工程技术-计算机:理论方法
CiteScore
1.90
自引率
0.00%
发文量
36
审稿时长
6-12 weeks
期刊介绍: TOCS is devoted to publishing original research from all areas of theoretical computer science, ranging from foundational areas such as computational complexity, to fundamental areas such as algorithms and data structures, to focused areas such as parallel and distributed algorithms and architectures.
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