{
  "id": "math/0611454",
  "version": "v3",
  "published": "2006-11-15T10:18:48.000Z",
  "updated": "2006-12-05T17:08:58.000Z",
  "title": "A fast algorithm to the conjugacy problem on generic braids",
  "authors": [
    "Ki Hyoung Ko",
    "Jang Won Lee"
  ],
  "comment": "12 pages, 1 figure. to appear in the Proceedings of the International Workshop on Knot Theory for Scientific Objects: OCAMI Studies Vol 1. Knot Theory for Scientific Objects",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Random braids that are formed by multiplying randomly chosen permutation braids are studied by analyzing their behavior under Garside's weighted decomposition and cycling. Using this analysis, we propose a polynomial-time algorithm to the conjugacy problem that is successful for random braids in overwhelming probability. As either the braid index or the number of permutation-braid factors increases, the success probability converges to 1 and so, contrary to the common belief, the distribution of hard instances for the conjugacy problem is getting sparser. We also prove a conjecture by Birman and Gonz\\'{a}lez-Meneses that any pseudo-Anosov braid can be made to have a special weighted decomposition after taking power and cycling. Moreover we give polynomial upper bounds for the power and the number of iterated cyclings required.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-12-05T17:08:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F10"
    ],
    "keywords": [
      "conjugacy problem",
      "generic braids",
      "fast algorithm",
      "random braids",
      "polynomial upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11454K"
    }
  }
}