Balanced allocations: The heavily loaded case

Document Type

Conference Proceeding

Publication Date

12-1-2000

Abstract

We investigate load balancing processes based on the multiple-choice paradigm. In these randomized processes m balls are inserted into n bins. In the classical single-choice variant each ball is placed simply into a randomly selected bin. In a multiple-choice process each ball can be placed into one out of d ≥ 2 randomly selected bins. It is well known that having more than one choice for each ball can improve the load balance significantly. In contrast to previous work on multiple-choice processes, we investigate the heavily loaded case, that is, we assume m ≫ n rather than m ≈ n. The best previously known results for the multiple-choice processes in the heavily loaded case were obtained by majorization from the single-choice process. This yields an upper bound of m/n + O(√m ln n/n). We show, however, that the multiple-choice processes are fundamentally different from the single-choice variant in that they have "short memory". The great consequence of this property is that the deviation of the multiple-choice processes from the optimal allocation (i.e., at most [m/n] balls in every bin) does not increase with the number of balls as in case of the single-choice process. In particular, we investigate the allocation obtained by two different multiple-choice allocation schemes, the original greedy scheme and the recently presented always-go-left scheme. We show that these schemes result in a maximum load of only m/n + O(ln ln n). We point out that our detailed bounds are tight up to additive constants. Furthermore, we investigate the two multiple-choice algorithms in a comparative study. We present a majorization result showing that the always-go-left scheme obtains a better load balancing than the greedy scheme for any choice of n, m, and d. © 2000 ACM.

Identifier

0033705066 (Scopus)

ISBN

[1581131844, 9781581131840]

Publication Title

Proceedings of the Annual ACM Symposium on Theory of Computing

External Full Text Location

https://doi.org/10.1145/335305.335411

ISSN

07378017

First Page

745

Last Page

754

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