# Chains-into-bins processes

Batu, Tugkan ORCID: 0000-0003-3914-4645, 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 Berlin / Heidelberg, pp. 314-325. ISBN 9783642192210

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Identification Number: 10.1007/978-3-642-19222-7_32

## 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 http://www.springerlink.com/ © 2011 Springer Mathematics Q Science > QA Mathematics 23 Jan 2012 14:46 16 May 2024 05:27 http://eprints.lse.ac.uk/id/eprint/41646