[
  {
    "id": "ads15-shifted-dgs-distance-cutoff",
    "categoryId": "dgs-shifted-distance-width",
    "paperId": "paper-eb07a87a7ce7",
    "year": 2015,
    "date": "2015-09-29",
    "datePrecision": "day",
    "time": {
      "coefficient": 1,
      "expression": "2^{n+o(n)} when log n log f(n)=o(n)"
    },
    "space": {
      "coefficient": 1,
      "expression": "At most 2^{n+o(n)} storage from the list algorithm"
    },
    "tags": [
      "classical",
      "provable",
      "worst case",
      "shifted DGS",
      "batch",
      "distance relative"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The full theorem has runtime 2^{n+O(log n log f(n))}. The coefficient 1 requires the displayed growth restriction on f; this is a cutoff sampler rather than arbitrary-width shifted DGS.",
    "extra": {
      "width": "s > dist(t,L)/f(n), efficiently computable f(n) >= n^{omega(1)} and log f(n)=o(n/log n)",
      "output": "At least m=rho_s(L-t)/max_{c in L/(2L)} rho_s(c-t) samples; m is instance- and width-dependent",
      "error": "Joint total-variation error 2^{-C n^2}, source constant C",
      "model": "Randomized classical; full list preparation included; polynomial input-size factors suppressed"
    },
    "evidence": {
      "url": "https://arxiv.org/abs/1504.01995v2",
      "locator": "Definition 2.11; Theorem 4.7, printed pp. 14–15",
      "sourceVersion": "arXiv:1504.01995v2, 29 September 2015"
    }
  }
]