NDLI: Quasirandom Load Balancing

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Gairing, Martin Sauerwald, Thomas Friedrich, Tobias
Copyright Year	2012
Abstract	We propose a simple distributed algorithm for balancing indivisible tokens on graphs. The algorithm is completely deterministic, though it tries to imitate (and enhance) a randomized algorithm by keeping the accumulated rounding errors as small as possible. Our new algorithm, surprisingly, closely approximates the idealized process (where the tokens are divisible) on important network topologies. On $d$-dimensional torus graphs with $n$ nodes it deviates from the idealized process only by an additive constant. In contrast, the randomized rounding approach of Friedrich and Sauerwald [Proceedings of the \textup41st Annual ACM Symposium on Theory of Computing, 2009, pp. 121--130] can deviate up to $\Omega(\operatorname{polylog}(n))$, and the deterministic algorithm of Rabani, Sinclair, and Wanka [Proceedings of the \textup39th Annual IEEE Symposium on Foundations of Computer Science, 1998, pp. 694--705] has a deviation of $\Omega(n^{1/d})$. This makes our quasirandom algorithm the first known algorithm for this setting, which is optimal both in time and achieved smoothness. We further show that on the hypercube as well, our algorithm has a smaller deviation from the idealized process than the previous algorithms. To prove these results, we derive several combinatorial and probabilistic results that we believe to be of independent interest. In particular, we show that first-passage probabilities of a random walk on a path with arbitrary weights can be expressed as a convolution of independent geometric probability distributions.
Starting Page	747
Ending Page	771
Page Count	25
File Format	PDF
ISSN	00975397
DOI	10.1137/100799216
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	41
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-08-16
Access Restriction	Subscribed
Subject Keyword	random walk load balancing Probability in computer science randomized algorithms Randomized algorithms quasirandomness Distributed algorithms distributed computing
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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