{
  "id": "rothvoss-venzin21-cvp-any-norm-approx",
  "categoryId": "cvp-constant-approximation-any-norm",
  "paperId": "rothvoss-venzin-2021",
  "year": 2021,
  "date": "2021-10-05",
  "time": {
    "coefficient": 0.802,
    "expression": "2^{(0.802 + ε)n}, for every fixed ε > 0"
  },
  "space": {
    "coefficient": 0.401,
    "expression": "2^{(0.401 + ε)n}"
  },
  "tags": [
    "arbitrary norms",
    "constant approximation"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Theorem 3.3 extends constant-factor approximate CVP to any norm and rank-n lattice. The approximation constant depends on ε. Lemma 3.1 removes the full-rank restriction with a controlled approximation loss.",
  "extra": {
    "norm": "Any norm from a centrally symmetric convex body",
    "approximation": "γ_ε = O_ε(1)",
    "preprocessing": "Included",
    "success": "Randomized approximation",
    "model": "Norm-oracle/convex-body representation as in §2; polynomial encoding and precision factors suppressed"
  },
  "evidence": {
    "url": "https://arxiv.org/pdf/2110.02387",
    "locator": "Theorem 3.3; Lemma 3.1; §2 representation conventions",
    "sourceVersion": "arXiv:2110.02387v1, 5 October 2021"
  }
}