[
  {
    "id": "drs14-bdd-radius-tradeoff",
    "categoryId": "bdd-preprocessing-tradeoffs",
    "paperId": "dadush-regev-stephens-davidowitz-2014",
    "year": 2014,
    "date": "2014-09-29",
    "datePrecision": "day",
    "time": {
      "coefficient": null,
      "expression": "2^{(log_2(e) alpha^2/(1-2alpha)^2)n+o(n)} per query"
    },
    "space": {
      "coefficient": null,
      "expression": "2^{(log_2(e) alpha^2/(1-2alpha)^2)n+o(n)} advice"
    },
    "tags": [
      "classical",
      "provable",
      "worst case",
      "preprocessing",
      "constant radius",
      "parameterized bound"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "For fixed alpha, suppressing polynomial factors gives this expression from Corollary 3.3. The first arXiv abstract already states N≈Õ(n exp(alpha²n/(1−2alpha)²)) advice vectors and Õ(nN) query time. At alpha=1/4 this specializes to exp(n/4+o(n)) time and advice, or base-2 coefficient log₂(e)/4≈0.3606737602. This example is part of the same tradeoff rather than a separate result or category. All costs here are per query or stored advice after unbounded target-independent preprocessing.",
    "extra": {
      "radius": "dist(t,L) <= alpha lambda_1(L)",
      "preprocessing": "Unbounded; source counts advice rather than its construction time",
      "advice": "N=O(alpha^2 n^2/(1-2alpha)^2 * exp(alpha^2 n/(1-2alpha)^2 + 4/(1-2alpha))) vectors",
      "parameters": "Any fixed 0 < alpha < 1/2; exact corollary allows Omega(1/sqrt(n)) < alpha < 1/2",
      "success": "Advice can be chosen to decode every promised target",
      "quarterRadiusExample": "alpha=1/4: query time and advice exp(n/4+o(n)) = 2^{(log₂(e)/4)n+o(n)}, coefficient ≈0.36067376022224085",
      "model": "Classical; query time after unbounded target-independent preprocessing"
    },
    "evidence": {
      "url": "https://www.noahsd.com/papers/cvpp.pdf",
      "locator": "Corollary 3.3, printed pp. 14–15; original v1 abstract includes the formula, alpha=1/4 is a direct substitution",
      "sourceVersion": "2014 author manuscript / arXiv:1409.8063; first arXiv date"
    }
  },
  {
    "id": "ghh26-bdd-reusable-tradeoff",
    "categoryId": "bdd-preprocessing-tradeoffs",
    "paperId": "paper-fd038bb9c63f",
    "year": 2026,
    "date": "2026-11-03",
    "datePrecision": "day",
    "time": {
      "coefficient": null,
      "expression": "2^{b n+o(n)} per target"
    },
    "space": {
      "coefficient": null,
      "expression": "2^{(log_2(4/3)/2)n+o(n)} bits"
    },
    "tags": [
      "classical",
      "provable",
      "worst case",
      "BDD",
      "preprocessing",
      "dual Gaussian batch",
      "parameterized bound"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The full-batch choice gives any fixed radius r < 0.3157071 with query exponent beta_G and preprocessing exponent alpha_G. The entire tradeoff is stored without a fabricated fixed score.",
    "extra": {
      "radius": "0 < r < sqrt(e b log(2))/(alpha A_KL), A_KL=2^{0.401}",
      "preprocessing": "2^{alpha_G n+o(n)}, alpha_G=(1/2)log_2(3/2)",
      "advice": "2^{beta_G n+o(n)} bits, beta_G=(1/2)log_2(4/3)",
      "parameters": "Feasible (alpha,b) in source Eq. (125), or full-batch (alpha,b)=(3/2,beta_G)",
      "success": "With probability 1-o(1), one advice string correctly decodes every rational target within r lambda_1(L)"
    },
    "evidence": {
      "url": "https://arxiv.org/abs/2611.04336v1",
      "locator": "Theorem 12.1, printed p. 59; Table 1, p. 7",
      "sourceVersion": "arXiv:2611.04336v1, 3 November 2026; first ePrint release 30 October not inspected separately"
    }
  }
]