Matchings via Random Greedy Independent Set: A Simpler Algorithm and Analysis
2026-08-11 • Data Structures and Algorithms
Data Structures and Algorithms
AI summaryⓘ
The authors show that a small change to a simple algorithm for picking independent sets in graphs can also find good matchings, which means pairing up nodes without overlaps. Their version simplifies a method used before by Assadi and others for handling changing graphs where edges can be added or removed. Unlike previous work, the authors avoid complicated math involving fractional matchings and provide a much shorter and clearer explanation for how well their method works.
maximum matchingrandomized greedy algorithmmaximal independent setgraph algorithmsapproximation algorithmdata streamsdynamic graphsfractional matching
Authors
Andrew McGregor
Abstract
We show that a simple extension of the randomized greedy maximal independent set algorithm yields a constant approximation for the maximum matching problem. The algorithm is a simplification of an algorithm used by Assadi et al. [JACM 2026] in the context of processing data streams in the dynamic setting where edges may be inserted and deleted. In contrast to the previous work, our analysis avoids consideration of fractional matchings and yields a significantly shorter and more direct proof of the approximation factor for the basic algorithm.