超宽字RAM的前身
Predecessor on the Ultra-Wide Word RAM
摘要：
我们考虑了计算的超宽字RAM模型的前题，该模型使用由$w^2$位组成的“超字”扩展了字RAM模型[TAMC，2015]。除了同时访问或修改$w$（可能不连续）内存地址的“分散”内存操作外，该模型还支持对超字的算术和布尔运算。超宽字RAM模型捕捉（和理想化）现代向量处理器架构。我们的主要结果是一个简单的，线性空间数据结构，支持在常数时间的前任和更新的摊销，预期常数时间。这改进了以前的常数时间解的空间，该解使用宇宙大小的空间。我们的结果保持即使在一个较弱的模型，其中超字组成的$w^{1+ε}$位的任何$ε> 0 $。它基于Willard [Inform.]的经典$x$ -快速trie数据结构的新实现。过程Lett. 17（2），1983]与支持快速并行查找的新字典数据结构相结合。
英文摘要：
We consider the predecessor problem on the ultra-wide word RAM model of computation, which extends the word RAM model with 'ultrawords' consisting of $w^2$ bits [TAMC, 2015]. The model supports arithmetic and boolean operations on ultrawords, in addition to 'scattered' memory operations that access or modify $w$ (potentially non-contiguous) memory addresses simultaneously. The ultra-wide word RAM model captures (and idealizes) modern vector processor architectures. Our main result is a simple, linear space data structure that supports predecessor in constant time and updates in amortized, expected constant time. This improves the space of the previous constant time solution that uses space in the order of the size of the universe. Our result holds even in a weaker model where ultrawords consist of $w^{1+ε}$ bits for any $ε> 0 $. It is based on a new implementation of the classic $x$-fast trie data structure of Willard [Inform. Process. Lett. 17(2), 1983] combined with a new dictionary data structure that supports fast parallel lookups.
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