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Near-perfect load balancing by randomized rounding (2009)
| Venue: | In 41st Annual ACM Symposium on Theory of Computing (STOC’09 |
| Citations: | 15 - 9 self |
BibTeX
@INPROCEEDINGS{Friedrich09near-perfectload,
author = {Tobias Friedrich and Thomas Sauerwald},
title = {Near-perfect load balancing by randomized rounding},
booktitle = {In 41st Annual ACM Symposium on Theory of Computing (STOC’09},
year = {2009},
pages = {121--130}
}
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Abstract
We consider and analyze a new algorithm for balancing indivisible loads on a distributed network with n processors. The aim is minimizing the discrepancy between the maximum and minimum load. In every time-step paired processors balance their load as evenly as possible. The direction of the excess token is chosen according to a randomized rounding of the participating loads. We prove that in comparison to the corresponding model of Rabani, Sinclair, and Wanka (1998) with arbitrary roundings, the randomization yields an improvement of roughly a square root of the achieved discrepancy in the same number of time-steps on all graphs. For the important case of expanders we can even achieve a constant discrepancy in O(log n(log log n) 3) rounds. This is optimal up to log log n-factors while the best previous algorithms in this setting either require Ω(log 2 n) time or can only achieve a logarithmic discrepancy. This result also demonstrates that with randomized rounding the difference between discrete and continuous load balancing vanishes almost completely.
Keyphrases
randomized rounding near-perfect load balancing log log excess token log n-factors arbitrary rounding indivisible load time-step paired processor constant discrepancy new algorithm continuous load balancing vanishes logarithmic discrepancy minimum load achieved discrepancy previous algorithm square root corresponding model important case distributed network
