超宽字RAM上的部分和
Partial Sums on the Ultra-Wide Word RAM
摘要：
我们考虑经典的部分和问题的超宽字RAM模型的计算。该模型扩展了经典的$w$ -位字RAM模型，使用长度为$w^2$位的特殊超字，支持标准算术和布尔运算以及可以访问存储器中$w$（非连续）位置的分散存储器访问操作。超宽字RAM模型捕获（并理想化）现代向量处理器架构。我们的主要结果是一个新的就地数据结构的部分和的问题，只存储一个常数的超字，除了输入和支持双对数时间的操作。这与问题的最佳已知时间界限（在多项式空间数据结构中）相匹配，同时将空间从超线性改进为超字的恒定数量。我们的结果是基于一个简单而优雅的字RAM数据结构，称为芬威克树。我们的主要技术贡献是一个新的高效并行超宽字RAM实现的芬威克树，这是可能的独立利益。
英文摘要：
We consider the classic partial sums 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 new in-place data structure for the partial sum problem that only stores a constant number of ultraword in addition to the input and supports operations in doubly logarithmic time. This matches the best known time bounds for the problem (among polynomial space data structures) while improving the space from superlinear to a constant number of ultrawords. Our results are based on a simple and elegant in-place word RAM data structure, known as the Fenwick tree. Our main technical contribution is a new efficient parallel ultra-wide word RAM implementation of the Fenwick tree, which is likely of independent interest.
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