Problem
Research questions and friction points this paper is trying to address.
parallel derandomization
work-efficiency
maximal independent set
maximal matching
(Δ+1)-coloring
True Work-Efficiency in Parallel Derandomization
🤖 AI Summary
本文解决了并行去随机化过程中工作量过大的问题，通过新方法实现了线性工作量O(m+n)，达到了真正的工作效率。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
parallel derandomization
linear work bounds
work-efficient
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