[
  {
    "id": "regev04-cvpp-poly-advice-decision",
    "categoryId": "cvpp-polynomial-advice-decision",
    "paperId": "regev-2004-cvpp",
    "year": 2004,
    "date": "2004-09-30",
    "time": {
      "coefficient": null,
      "expression": "poly(input size) query time"
    },
    "space": {
      "coefficient": null,
      "expression": "Polynomial-size lattice-dependent advice"
    },
    "tags": [
      "preprocessing",
      "polynomial advice",
      "decision"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Section V explicitly solves Euclidean GAPCVPP_n. This row tracks a gap decision and distance-estimation guarantee; it does not claim an n-approximate lattice-vector finder.",
    "extra": {
      "norm": "Euclidean ℓ₂",
      "approximation": "Gap factor n",
      "preprocessing": "Unrestricted; depends only on the lattice",
      "advice": "Polynomial-size lattice description",
      "success": "Polynomial-time threshold decision"
    },
    "evidence": {
      "url": "https://cims.nyu.edu/~regev/papers/cvpp.pdf",
      "locator": "§II Definition 2.5; §V Upper Bound, GAPCVPP_n",
      "sourceVersion": "IEEE Transactions on Information Theory 50(9), September 2004"
    },
    "datePrecision": "month"
  },
  {
    "id": "aharonov-regev05-cvpp-poly-advice-decision",
    "categoryId": "cvpp-polynomial-advice-decision",
    "paperId": "aharonov-regev-2005",
    "year": 2005,
    "date": "2005-09-08",
    "time": {
      "coefficient": null,
      "expression": "poly(input size) query time; degree may depend on c"
    },
    "space": {
      "coefficient": null,
      "expression": "poly(input size) advice; degree may depend on c"
    },
    "tags": [
      "preprocessing",
      "polynomial advice",
      "decision"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Theorem 1.4 gives a polynomial query algorithm for GapCVPP with factor c√(n/log n) for every fixed c > 0. Section 5 computes an estimator using polynomially many preprocessed dual-lattice vectors.",
    "extra": {
      "norm": "Euclidean ℓ₂",
      "approximation": "c√(n/log n), for every fixed c > 0",
      "preprocessing": "Unbounded; lattice-only advice",
      "advice": "N = poly(n) dual-lattice vectors; degree depends on c",
      "success": "Polynomial-time gap decision from suitable fixed advice"
    },
    "evidence": {
      "url": "https://cims.nyu.edu/~regev/papers/cvpconp.pdf",
      "locator": "Theorem 1.4 and §5 proof",
      "sourceVersion": "Author manuscript dated 8 September 2005; JACM 52(5), 2005"
    }
  }
]