[
  {
    "id": "adrs15-gapsvp193",
    "categoryId": "svp-gap-euclidean-parameterized",
    "paperId": "paper-86925aff6e6c",
    "year": 2015,
    "date": "2014-12-26",
    "time": {
      "coefficient": null,
      "expression": "2^{n/2+o(n)} for gap factor γ = 1.93"
    },
    "space": {
      "coefficient": 0.5,
      "expression": "2^{0.5 n + o(n)}"
    },
    "tags": [
      "classical",
      "provable",
      "worst case",
      "GapSVP",
      "approximate",
      "decision"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The above-smoothing sampler implies a 1.93-approximate decision-SVP algorithm in the stated total time and space. The source does not claim an approximate shortest vector with this cost. The factor is retained as an entry parameter; bounds for different gap factors are not assigned a common numerical rank.",
    "extra": {
      "norm": "Euclidean ℓ₂",
      "approximation": "γ = 1.93",
      "output": "Promise decision: λ₁(L) ≤ r versus λ₁(L) > γr",
      "model": "Randomized classical",
      "reference": "ADRS15",
      "timeExponentAtStatedGuarantee": "0.5"
    },
    "evidence": {
      "url": "https://arxiv.org/abs/1412.7994v1",
      "locator": "Abstract, above-smoothing DGS and 1.93-approximate decision-SVP consequence",
      "sourceVersion": "arXiv:1412.7994v1, 26 December 2014"
    }
  }
]