{
  "id": "kannan87-cvp-enumeration",
  "categoryId": "cvp-polynomial-space",
  "paperId": "kannan-1987",
  "year": 1987,
  "date": "1987-12-31",
  "time": {
    "coefficient": 1,
    "expression": "O(n^n s) arithmetic operations = n^{n+o(n)} poly(s)"
  },
  "space": {
    "coefficient": null,
    "expression": "poly(s)"
  },
  "tags": [
    "polynomial space",
    "exact",
    "enumeration"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Theorem 4.5 gives exact CVP in O(n^n s) arithmetic operations, where s is the input bit length. This establishes leading coefficient 1 on the n log n scale. The later n^{n/2+o(n)} CVP analysis is not backdated to Kannan.",
  "extra": {
    "norm": "Euclidean ℓ₂",
    "preprocessing": "Included; arbitrary input basis",
    "target": "Arbitrary target",
    "model": "Deterministic enumeration; bounded-bit arithmetic",
    "success": "Exact output",
    "costScale": "n log₂ n"
  },
  "evidence": {
    "url": "https://www.math.ucdavis.edu/~deloera/MISC/LA-BIBLIO/trunk/Kannan/Kannan1.pdf",
    "locator": "§4, Theorem 4.5; polynomial bit-length bounds in the following paragraph",
    "sourceVersion": "Mathematics of Operations Research 12(3), 1987"
  },
  "datePrecision": "year"
}