Batu, Tugkan, Berenbrink, Petra and Cooper, Colin
(2011)
*Chains-into-bins processes.*
In: Iliopoulos, Costas S. and Smyth, William F., (eds.)
Combinatorial Algorithms.
Lecture notes in computer science(6460).
Springer, pp. 314-325.
ISBN 9783642192210

## Abstract

The study of balls-into-bins processes or 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 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 ℓ, so that there are m ℓ balls in total. We assume the chains cannot be broken, and that the balls in one chain have to be allocated to ℓ 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 ≥ 2 and m·ℓ= O(n), the maximum load is ((ln ln m)/ln d) + O(1) with probability 1−O(1md−1) .

Item Type: | Book Section |
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Official URL: | http://www.springerlink.com/ |

Additional Information: | © 2011 Springer |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Identification Number: | Published item via DOI |

Date Deposited: | 23 Jan 2012 14:46 |

URL: | http://eprints.lse.ac.uk/41646/ |

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