{
  "id": "2301.10637",
  "version": "v1",
  "published": "2023-01-25T15:21:35.000Z",
  "updated": "2023-01-25T15:21:35.000Z",
  "title": "Bit-complexity estimates in geometric programming, and application to the polynomial-time computation of the spectral radius of nonnegative tensors",
  "authors": [
    "Shmuel Friedland",
    "Stéphane Gaubert"
  ],
  "comment": "26 pages",
  "categories": [
    "math.OC",
    "cs.CC"
  ],
  "abstract": "We show that the spectral radius of nonnegative tensors can be approximated within $\\varepsilon$ error in polynomial time. This implies that the maximum of a nonnegative homogeneous $d$-form in the unit ball with respect to $d$-H\\\"older norm can be approximated in polynomial time. These results are deduced by establishing bit-size estimates for the near-minimizers of functions given by suprema of finitely many log-Laplace transforms of discrete nonnegative measures on $\\mathbb{R}^n$. Hence, some known upper bounds for the clique number of hypergraphs are polynomially computable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-25T15:21:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C65",
      "15A69",
      "68W25"
    ],
    "keywords": [
      "spectral radius",
      "nonnegative tensors",
      "bit-complexity estimates",
      "polynomial-time computation",
      "geometric programming"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}