A Simple Average-case Analysis of Recursive Randomized Greedy MIS
arXiv:2604.01462v1 Announce Type: new Abstract: We revisit the complexity analysis of the recursive version of the randomized greedy algorithm for computing a maximal independent set (MIS), originally analyzed by Yoshida, Yamamoto, and Ito (2009). They showed that, on average per vertex, the expected number of recursive calls made by this algorithm is upper bounded by the average degree of the input graph. While their analysis is clever and intricate, we provide a significantly simpler alternative that achieves the same guarantee. Our analysis is inspired by the recent work of Dalirrooyfard, Makarychev, and Mitrovi\'c (2024), who developed a potential-function-based argument to analyze a new algorithm for correlation clustering. We adapt this approach to the MIS setting, yielding a more di
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Abstract:We revisit the complexity analysis of the recursive version of the randomized greedy algorithm for computing a maximal independent set (MIS), originally analyzed by Yoshida, Yamamoto, and Ito (2009). They showed that, on average per vertex, the expected number of recursive calls made by this algorithm is upper bounded by the average degree of the input graph. While their analysis is clever and intricate, we provide a significantly simpler alternative that achieves the same guarantee. Our analysis is inspired by the recent work of Dalirrooyfard, Makarychev, and Mitrović (2024), who developed a potential-function-based argument to analyze a new algorithm for correlation clustering. We adapt this approach to the MIS setting, yielding a more direct and arguably more transparent analysis of the recursive randomized greedy MIS algorithm.
Subjects:
Data Structures and Algorithms (cs.DS)
Cite as: arXiv:2604.01462 [cs.DS]
(or arXiv:2604.01462v1 [cs.DS] for this version)
https://doi.org/10.48550/arXiv.2604.01462
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Slobodan Mitrović [view email] [v1] Wed, 1 Apr 2026 23:16:16 UTC (17 KB)
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