论文标题
部分可观测时空混沌系统的无模型预测
An Optimal Decentralized $(Δ+ 1)$-Coloring Algorithm
论文作者
论文摘要
考虑$ N $顶点的图形以下简单着色算法。每个顶点从$ \ {1，\ dotsc，δ（g） + 1 \} $随机选择颜色。当存在一个冲突的顶点时，选择一个均匀的顶点，然后随机地重新涂上它。该算法由Bhartia等人引入。 [Mobihoc'16]用于WiFi-Networks中的频道选择。我们表明，该算法总是在预期的$ o（n \logδ）$ steps中收敛到适当的着色，这是最佳的，并且证明了Chakrabarty和Supinski [Sosa'20]的猜想。
Consider the following simple coloring algorithm for a graph on $n$ vertices. Each vertex chooses a color from $\{1, \dotsc, Δ(G) + 1\}$ uniformly at random. While there exists a conflicted vertex choose one such vertex uniformly at random and recolor it with a randomly chosen color. This algorithm was introduced by Bhartia et al. [MOBIHOC'16] for channel selection in WIFI-networks. We show that this algorithm always converges to a proper coloring in expected $O(n \log Δ)$ steps, which is optimal and proves a conjecture of Chakrabarty and Supinski [SOSA'20].
