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Improved distributed $$\Delta $$ Δ -coloring
Distributed Computing ( IF 1.3 ) Pub Date : 2021-07-09 , DOI: 10.1007/s00446-021-00397-4
Mohsen Ghaffari 1 , Juho Hirvonen 2 , Fabian Kuhn 3 , Yannic Maus 4
Affiliation  

We present a randomized distributed algorithm that computes a \(\Delta \)-coloring in any non-complete graph with maximum degree \(\Delta \ge 4\) in \(O(\log \Delta ) + 2^{O(\sqrt{\log \log n})}\) rounds, as well as a randomized algorithm that computes a \(\Delta \)-coloring in \(O((\log \log n)^2)\) rounds when \(\Delta \in [3, O(1)]\). Both these algorithms improve on an \(O(\log ^3 n / \log \Delta )\)-round algorithm of Panconesi and Srinivasan (STOC’93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an \(\Omega (\log \log n)\) round lower bound of Brandt et al. (STOC’16).



中文翻译:

改进的分布式 $$\Delta $$ Δ -coloring

我们提出了一个随机化分布式算法,计算一个\(\德尔塔\) -coloring在任何非完全图最大度\(\德尔塔\ GE 4 \)\(O(\日志\德尔塔)+ 2 ^ {ö (\sqrt{\log \log n})}\)轮,以及计算\(\Delta \) -着色\(O((\log \log n)^2)\)的随机算法当\(\Delta \in [3, O(1)]\) 时舍入。这两种算法都改进了Panconesi 和 Srinivasan (STOC'93)的\(O(\log ^3 n / \log \Delta )\)轮算法,该算法在过去 25 年中一直是最先进的。此外,后一种算法(指数上)更接近\(\Omega (\log \log n)\)Brandt 等人的圆形下限。(STOC'16)。

更新日期:2021-07-09
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