{
  "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"
  }
}