发表机构
Univ Gustave Eiffel, CNRS, LIGM（巴黎-东马恩拉瓦莱大学，法国国家科学研究中心，信息学与多学科实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文对基于SIMD的哈希表实现进行细粒度理论分析，采用Wormald的微分方程技术精确刻画动态，以高概率给出结果，并与实验高度吻合。
AI 中文摘要
近年来，工程师们开发了多种经典哈希表方案的变体，以利用处理器内部并行性，通过SIMD指令同时操作多个字节。在较小的额外内存开销下，这能带来显著的加速，使其在实际中需要极高性能时越来越受欢迎。在本文中，我们对这类哈希表的动态进行了详细的理论分析。从方法论的角度，我们使用并改编了Wormald在1990年代为研究动态图而开发的技术。这种方法可适用于多种变体，通过微分方程组捕捉数据结构的动态，使我们能够精确估计感兴趣的量。尽管系统复杂，我们提供了这些系统解的显式描述，且这些解可以高效地进行数值近似。我们的主要结果以高概率陈述，这比平均情况分析精确得多，并且与实验结果吻合得非常好，即使对于中等规模的哈希表也是如此。
英文摘要
In recent years, several variants of classical hash table schemes have been developed by engineers in order to take advantage of the processor's internal parallelism using SIMD instructions, which make it possible to operate on multiple bytes simultaneously. At a small additional memory cost, this enables a significant speedup, making it a data structure that is increasingly popular in practice, when very high performance is required. In this article, we provide a detailed theoretical analysis of the dynamics of such hash tables. From a methodological standpoint, we use and adapt a technique developed by Wormald in the 1990s to study dynamic graphs. This approach, which can be adapted to many variants, enables us to accurately estimate the quantities of interest by capturing the dynamics of the data structure through systems of differential equations. Although complex, we provide an explicit description of the solutions of these systems, which can furthermore be efficiently approximated numerically. Our main results are stated with high probability, which is significantly more precise than average-case analyses, and they match experimental results remarkably well, even for hash tables of moderate size.
