{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R352",
  "content_hash": null,
  "slug": "gtc-claim-search-cost",
  "type": "claim",
  "title": "Exhaustive search cost multiplies by about 4.6 per vertex",
  "summary": "Search nodes per size: n=10: 8,264, n=11: 28,462, n=12: 97,710, n=13: 587,455, n=14: 2,503,495, n=15: 16,305,531. Cost grows by a factor of 4.6 per vertex while the tree count grows by 2.4.",
  "relevance": "For Graceful tree conjecture, record gtc-claim-search-cost (“Exhaustive search cost multiplies by about 4.6 per vertex”) records a bound, answer, status fact, or structural consequence. The record states: Search nodes per size: n=10: 8,264, n=11: 28,462, n=12: 97,710, n=13: 587,455, n=14: 2,503,495, n=15: 16,305,531.",
  "relevance_source": "recorded",
  "body": "Backtracking nodes used by the graceful search, by tree size: n=10: 8,264, n=11: 28,462, n=12: 97,710, n=13: 587,455, n=14: 2,503,495, n=15: 16,305,531.\n\nOver that range the node count grows by 4.6 per vertex (the last single step is 6.5), against a tree-count growth of 2.4. The per-tree cost is rising as well as the number of trees.\n\nCarrying that factor from n=15 to the published bound of 35 vertices means roughly 2e+13 times the work of the run recorded here. A plain exhaustive sweep does not reach that bound, which is consistent with the published verification having used constraint propagation and randomized search. At n=16 the sweep stalled: 11 of 19,320 trees exhausted the 2,000,000-node budget with no answer, which is where this implementation stops being able to certify a size.",
  "status": "reproduced",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "search cost measured on trees of 10 to 15 vertices",
    "bounds": {
      "n": {
        "max": 15,
        "min": 10
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1403.1564",
      "locator": "research/graceful-trees/checks.py --max-n 15"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1403.1564",
    "locator": "research/graceful-trees/checks.py --max-n 15"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R344",
      "title": "Settle the conjecture by extending exhaustive verification",
      "object_type": "attempt",
      "relation": "constrains",
      "direction": "outgoing"
    },
    {
      "slug": "R341",
      "title": "Search cost by tree size",
      "object_type": "artifact",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "graceful-tree-conjecture",
      "title": "graceful tree conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}