Finding independent sets of maximum size in fixed graphs is well known to be an NP-hard task. Using scaling limits, we characterise the asymptotics of sequential degree-greedy explorations and provide sufficient conditions for this algorithm to find an independent set of asymptotically optimal size in large sparse random graphs with given degree sequences. In the special case of sparse Erdos-Renyi graphs, our results allow to give a simple proof of the so-called $e$-phenomenon identified by Karp and Sipser for matchings and to give an alternative characterisation of the asymptotic independence number.

中文翻译：

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配置模型图中独立集的贪婪度发现的渐近最优性

众所周知，在固定图中寻找最大尺寸的独立集是一项 NP-hard 任务。使用缩放限制，我们描述了连续度贪婪探索的渐近性，并为该算法提供了充分条件，以在具有给定度数序列的大型稀疏随机图中找到一组独立的渐近最优大小。在稀疏 Erdos-Renyi 图的特殊情况下，我们的结果允许对 Karp 和 Sipser 为匹配识别的所谓 $e$-现象提供一个简单的证明，并给出渐近独立数的替代表征。