Optimality of Greedy for Single-Pass Semi-Streaming Matching
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 .
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Streaming algorithms
- Posed by
- Feigenbaum, Kannan, McGregor, Suri, Zhang
- Year posed
- 2005
- Years open
- 21y
- Solved
- 2026-07-20
- Model
- Claude Fable 5, GPT-5.6 Sol, Claude Opus 5, Gemini
- Vendor
- Anthropic / OpenAI / Google
- Collaborators
- Sepehr Assadi, Max Jiang, Mars Xiang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 35 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
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.
Verification
arXiv preprint by established authors in the area, building on their own earlier blueprint framework; not yet peer-reviewed.
Source
arXiv:2607.14656 - Semi-Streaming Matching in a Single Pass II: Greedy is Optimal