{
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  "problem_id": "vibemathed:semi-streaming-matching-greedy-optimal",
  "title": "Optimality of Greedy for Single-Pass Semi-Streaming Matching",
  "canonical_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 $1/2$.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
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      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-07-20T00:00:00.000Z",
      "title": "arXiv:2607.14656 - Semi-Streaming Matching in a Single Pass II: Greedy is Optimal",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "provider": "Anthropic / OpenAI / Google",
      "attempted_at": "2026-07-20T00:00:00.000Z",
      "human_collaborators": [
        "Sepehr Assadi",
        "Max Jiang",
        "Mars Xiang"
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      "verifier": "VibeMathed (source-reported label)",
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      "note": "arXiv preprint by established authors in the area, building on their own earlier blueprint framework; not yet peer-reviewed.",
      "sources": [
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          "label": "arXiv:2607.14656 - Semi-Streaming Matching in a Single Pass II: Greedy is Optimal",
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      "label": "arXiv:2607.14656 - Semi-Streaming Matching in a Single Pass II: Greedy is Optimal",
      "url": "https://arxiv.org/abs/2607.14656",
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      "license": null
    },
    {
      "label": "VibeMathed: Optimality of Greedy for Single-Pass Semi-Streaming Matching",
      "url": "https://vibemathed.com/problem/semi-streaming-matching-greedy-optimal",
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    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}