Optimality of Greedy for Single-Pass Semi-Streaming Matching

Precise statement

Can any single-pass semi-streaming algorithm beat the naive greedy $1/2$-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 $1/2$.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

Claude Fable 5, GPT-5.6 Sol, Claude Opus 5, Gemini

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.

Provider: Anthropic / OpenAI / Google · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

arXiv preprint by established authors in the area, building on their own earlier blueprint framework; not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-20

   arXiv:2607.14656 - Semi-Streaming Matching in a Single Pass II: Greedy is Optimal

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.