Parallel randomized load balancing: A lower bound for a more general model

We extend the lower bound of Adler et al. (1998) [1] and Berenbrink et al. (1999) [2] for parallel randomized load balancing algorithms. The setting in these asynchronous and distributed algorithms is of n balls and n bins. The algorithms begin by each ball choosing d bins independently and unifor...

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Bibliographic Details
Published in:	Theoretical computer science Vol. 412; no. 22; pp. 2398 - 2408
Main Authors:	Even, Guy, Medina, Moti
Format:	Journal Article
Language:	English
Published:	Oxford Elsevier B.V 13.05.2011 Elsevier
Subjects:	Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Balls and bins Bins Collisions Computer science; control theory; systems Computer simulation Exact sciences and technology Load balancing Lower bounds Miscellaneous Proving Static randomized parallel allocation Symmetry Theoretical computing Topology Balls and bins Lower bounds Load balancing Static randomized parallel allocation Lower bound Parallel algorithm Asynchronous Computer theory Static allocation Decision Assignment Maximum Distributed algorithm Proof Communication Symmetry
ISSN:	0304-3975, 1879-2294
Online Access:	Get full text
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Summary:	We extend the lower bound of Adler et al. (1998) [1] and Berenbrink et al. (1999) [2] for parallel randomized load balancing algorithms. The setting in these asynchronous and distributed algorithms is of n balls and n bins. The algorithms begin by each ball choosing d bins independently and uniformly at random. The balls and bins communicate to determine the assignment of each ball to a bin. The goal is to minimize the maximum load, i.e., the number of balls that are assigned to the same bin. In Adler et al. (1998) [1] and Berenbrink et al. (1999) [2], a lower bound of Ω ( log n / log log n r ) is proved if the communication is limited to r rounds. Three assumptions appear in the proofs in Adler et al. (1998) [1] and Berenbrink et al. (1999) [2]: the topological assumption, random choices of confused balls, and symmetry. The topological assumption states that each ball’s decision is based only on collisions between choices of balls. The confused ball assumption states that if a ball obtains the same topological information from all its chosen bins, then the ball commits to one of the chosen bins by flipping a fair coin. The symmetry assumption states that all the balls run identical algorithms, the same assumption holds for the bins. We extend the proof of the lower bound so that it holds without these three assumptions. This lower bound applies to every parallel randomized load balancing algorithm we are aware of (Adler et al., 1998 [1]; Berenbrink et al., 1999 [2]; Stemann, 1996 [3]; Even and Medina, 2009 [4]).
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2011.01.033