We consider the dynamic range minimum problem on the ultra-wide word RAM model of computation. This model extends the classic $w$-bit word RAM model with special ultrawords of length $w^2$ bits that support standard arithmetic and boolean operation and scattered memory access operations that can access $w$ (non-contiguous) locations in memory. The ultra-wide word RAM model captures (and idealizes) modern vector processor architectures. Our main result is a linear space data structure that supports range minimum queries and updates in $O(\log \log \log n)$ time. This exponentially improves the time of existing techniques. Our result is based on a simple reduction to prefix minimum computations on sequences $O(\log n)$ words combined with a new parallel, recursive implementation of these.

翻译：本文研究超宽字RAM计算模型上的动态范围最小值问题。该模型在经典的$w$位字RAM模型基础上进行了扩展，引入了长度为$w^2$位的特殊超宽字，支持标准算术与布尔运算，以及能够同时访问内存中$w$个（非连续）位置的分散内存访问操作。超宽字RAM模型刻画（并理想化）了现代向量处理器架构。我们的主要成果是提出一种线性空间数据结构，该结构能够在$O(\log \log \log n)$时间内支持范围最小值查询与更新操作，这相对于现有技术实现了指数级的时间改进。该结果基于对$O(\log n)$字长序列的前缀最小值计算的简化，并结合了新颖的并行递归实现方法。