Optimality of Greedy for Single-Pass Semi-Streaming Matching
Statement
Can any single-pass semi-streaming algorithm beat the naive greedy -approximation for maximum matching? No. No single-pass semi-streaming algorithm, deterministic or randomized, achieves a better-than-half approximation, so greedy is optimal. The same construction settles the optimal competitive ratio of online matching with preemption at .
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Sepehr Assadi, Max Jiang and Mars Xiang, using Claude Fable 5, GPT-5.6 Sol, Claude Opus 5, GeminiThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The AI acknowledgement is unusually precise. The authors supplied an optimal solution to a relaxation of blueprints, and a combination of Claude Fable and GPT-5.6 Sol gave the idea of using random walks to lift that solution from the relaxation to blueprints. The authors write that these random walks formed the crux of their blueprints. GPT-5.6 Sol also solved the optimization problem behind Lemma 3.1 after the authors directed it to formulate the problem as a linear program, though the proof in the paper is the authors' own. The authors state that no AI-generated text appears in the paper and that they wrote all statements and proofs themselves.
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