The random greedy algorithm for finding a maximal independent set in a graph constructs a maximal independent set by inspecting the graph's vertices in a random order, adding the current vertex to the independent set if it is not adjacent to any previously added vertex. In this paper, we present a general framework for computing the asymptotic density of the random greedy independent set for sequences of (possibly random) graphs by employing a notion of local convergence. We use this framework to give straightforward proofs for results on previously studied families of graphs, like paths and binomial random graphs, and to study new ones, like random trees and sparse random planar graphs. We conclude by analysing the random greedy algorithm more closely when the base graph is a tree.

中文翻译：

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通过局部限制的贪婪最大独立集

用于在图中查找最大独立集的随机贪婪算法通过以随机顺序检查图的顶点来构造最大独立集，如果当前顶点不与任何先前添加的顶点相邻，则将当前顶点添加到独立集。在本文中，我们提出了一个通用框架，通过采用局部收敛的概念来计算（可能是随机的）图序列的随机贪婪独立集的渐近密度。我们使用这个框架为之前研究的图族（如路径和二项式随机图）的结果提供直接的证明，并研究新的图族，如随机树和稀疏随机平面图。当基础图是树时，我们通过更仔细地分析随机贪婪算法得出结论。