AI 中文总结
本文针对并行去随机化的工作效率问题，在Ghaffari等人工作基础上，将工作开销优化至线性界O(m+n)，实现了真正工作高效的并行去随机化。
AI 中文摘要
现有并行去随机化技术长期存在至少多对数级工作开销的局限，例如针对最大独立集、最大匹配、(Δ+1)着色（Δ为图的最大度）等基础常用问题，n个顶点m条边的图上，深度为多对数级的最优确定性并行算法需Ω((m+n)poly(log n))工作，参见Luby[FOCS '88]，因此这些算法至少需要poly(log n)个处理器才能优于简单的单处理器算法。近期Ghaffari与Grunau[FOCS '25]提出新的并行去随机化方法，将开销从poly(log n)大幅降至poly(log log n)，工作界达到O((m+n)poly(log log n))。本文解决该研究方向，获得线性工作界O(m+n)，实现了真正工作高效的并行去随机化。
英文摘要
A longstanding limitation of known techniques for parallel derandomization was that they incurred at least polylogarithmic overhead in work. For instance, for fundamental and frequently used problems such as maximal independent set, maximal matching, and $(Δ+1)$-coloring, where $Δ$ denotes the maximum degree of the graph, the best-known deterministic parallel algorithms with polylogarithmic depth used $Ω((m+n)\mathrm{poly}(\log n))$ work on $n$-vertex, $m$-edge graphs; see, e.g., Luby [FOCS '88]. Consequently, at least $\mathrm{poly}(\log n)$ processors were needed for these algorithms to outperform straightforward single-processor algorithms. Recently, Ghaffari and Grunau [FOCS '25] introduced a new parallel derandomization method that substantially reduced the overhead from $\mathrm{poly}(\log n)$ to $\mathrm{poly}(\log\log n)$, achieving work bounds of $O((m+n)\mathrm{poly}(\log\log n))$. In this paper, we settle this line of research by obtaining linear work bounds of $O(m+n)$, thereby achieving truly work-efficient parallel derandomization.
