{
  "id": "1908.10278",
  "version": "v1",
  "published": "2019-08-27T15:34:00.000Z",
  "updated": "2019-08-27T15:34:00.000Z",
  "title": "The power of $d$-thinning in load balancing",
  "authors": [
    "Ohad N. Feldheim",
    "Jiange Li"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In the classical balls-and-bins model, $m$ balls are allocated into $n$ bins one by one uniformly at random. In this note, we consider the $d$-thinning variant of this model, in which the process is regulated in an on-line fashion as follows. For each ball, after a random allocation bin has been generated, an overseer may decide, based on all previous history, whether to accept or reject this allocation. However, one of every $d$ consecutive suggested allocations must be accepted. The \\emph{maximum load} of the model is the number of balls in the most loaded bin. We show that after $\\Theta(n)$ balls have been allocated, the least maximum load achievable with high probability is $(d+o(1))(d\\log n/\\log\\log n)^{1/d}$. This is in contrast with the related two-choice model, in which the number of alternative choices offered to the overseer merely affects the achievable maximum load by a multiplicative constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-27T15:34:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "load balancing",
      "random allocation bin",
      "on-line fashion",
      "classical balls-and-bins model",
      "high probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}