{
  "id": "naszodi-venzin19-cvp-euclidean-near-exact",
  "categoryId": "cvp-approximate-euclidean-parameterized",
  "paperId": "naszodi-venzin-2019",
  "year": 2022,
  "date": "2019-08-22",
  "datePrecision": "day",
  "time": {
    "coefficient": null,
    "expression": "2^{O(n)} (1/δ)^{n/2} poly(input size, log(1/δ)), 0<δ<1"
  },
  "space": {
    "coefficient": 1,
    "expression": "2^n poly(input size), using the general-norm constant-approximation solver"
  },
  "tags": [
    "classical",
    "provable",
    "worst case",
    "Euclidean",
    "approximate search",
    "covering",
    "parameterized approximation"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "The Euclidean specialization p=2 of the smoothness-based covering algorithm improves the dependence on approximation accuracy. This is an alternative algorithmic bound rather than a claim to beat the already known 2^{n+o(n)} exact Euclidean CVP bound. No numerical leading coefficient is inferred from the hidden 2^{O(n)} factor.",
  "extra": {
    "norm": "Euclidean ℓ₂ (p=2 specialization)",
    "approximation": "Distance at most (1+δ) dist(t,L), for 0<δ<1",
    "preprocessing": "Included, using a general-norm 2-CVP subroutine; covering generated locally",
    "success": "Randomized success at least 1-2^{-n}; deterministic net enumeration is also discussed"
  },
  "evidence": {
    "url": "https://arxiv.org/pdf/1908.08384v1",
    "locator": "Abstract; §1, item (5); Theorem 4.6, using the ℓ₂ modulus of smoothness with power q=2",
    "sourceVersion": "arXiv:1908.08384v1, 22 August 2019"
  }
}