Batu, Tugkan, Berenbrink, Petra and Cooper, Colin
(2010)
*Chains-into-bins processes.*
.
arXiv.org.

## Abstract

The study of {\em balls-into-bins processes} or {\em occupancy problems} has a long history. These processes can be used to translate realistic problems into mathematical ones in a natural way. In general, the goal of a balls-into-bins process is to allocate a set of independent objects (tasks, jobs, balls) to a set of resources (servers, bins, urns) and, thereby, to minimize the maximum load. In this paper, we analyze the maximum load for the {\em chains-into-bins} problem, which is defined as follows. There are $n$ bins, and $m$ objects to be allocated. Each object consists of balls connected into a chain of length $\ell$, so that there are $m \ell$ balls in total. We assume the chains cannot be broken, and that the balls in one chain have to be allocated to $\ell$ consecutive bins. We allow each chain $d$ independent and uniformly random bin choices for its starting position. The chain is allocated using the rule that the maximum load of any bin receiving a ball of that chain is minimized. We show that, for $d \ge 2$ and $m\cdot\ell=O(n)$, the maximum load is $((\ln \ln m)/\ln d) +O(1)$ with probability $1-\tilde O(1/m^{d-1})$.

Item Type: | Monograph (Report) |
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Official URL: | http://arxiv.org/abs/1005.2616v1 |

Additional Information: | © 2010 The authors |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 10 Jan 2011 10:28 |

Last Modified: | 30 Jan 2019 22:56 |

URI: | http://eprints.lse.ac.uk/id/eprint/31302 |

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