Matchings via Random Greedy Independent Set: A Simpler Algorithm and Analysis

2026-08-11

AI Summary

This work addresses the problem of obtaining a constant-factor approximation for maximum matching in graphs. By extending the randomized greedy maximal independent set algorithm to the matching setting, the paper proposes a significantly simpler constant-approximation algorithm. The key innovation lies in abandoning the conventional fractional matching analysis framework and instead employing a direct combinatorial optimization argument, which greatly streamlines the proof of the approximation ratio. This approach not only preserves the theoretical guarantees but also substantially reduces the analytical complexity, offering a clearer and more efficient avenue for approximating the maximum matching problem.

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.

Problem

• maximum matching
• randomized greedy
• approximation algorithm
• dynamic graph streams
• independent set

Innovation

• randomized greedy
• maximal independent set
• maximum matching
• approximation algorithm
• streaming algorithms