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Ballanced allocations with heterogeneous bins
 In Proceedings of the Sympostiom on Parallel Algorithms and Architecture (SPAA
"... Ballsintobins processes are a useful and common abstraction for many loadbalancing related problems. A well known paradigm for load balancing in distributed or parallel servers is the ”multiple choice paradigm ” where an item (ball) is put in the less loaded out of d uniformly chosen servers (bin ..."
Abstract

Cited by 8 (3 self)
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Ballsintobins processes are a useful and common abstraction for many loadbalancing related problems. A well known paradigm for load balancing in distributed or parallel servers is the ”multiple choice paradigm ” where an item (ball) is put in the less loaded out of d uniformly chosen servers (bins). In many applications however the uniformity of the sampling probability is not guaranteed. If the system is heterogenous or dynamic it may be the case that some bins are sampled with a higher probability than others. We investigate the power of the multiple choice paradigm in the setting where bins are not sampled from the uniform distribution. Byers et al [5] showed that a logarithmic imbalance in the sampling probability could be tolerated, as long as the number of balls is linear in the number of bins. We show that if the number of balls is much larger than the number of bins, this ceases to be the case. Given a probability over bins, we prove tight upper and lower bounds for the number of choices needed in the 1outofd scheme in order to maintain a balanced allocations when the number of items is arbitrarily high.
Balanced Allocations: The Weighted Case
, 2008
"... We investigate ballsandbins processes where m weighted balls are placed into n bins using the “power of two choices ” paradigm, whereby a ball is inserted into the less loaded of two randomly chosen bins. The case where each of the m balls has unit weight had been studied extensively. In a seminal ..."
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Cited by 7 (2 self)
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We investigate ballsandbins processes where m weighted balls are placed into n bins using the “power of two choices ” paradigm, whereby a ball is inserted into the less loaded of two randomly chosen bins. The case where each of the m balls has unit weight had been studied extensively. In a seminal paper Azar et al. [2] showed that when m = n the most loaded bin has Θ(log log n) balls with high probability. Surprisingly, the gap in load between the heaviest bin and the average bin does not increase with m and was shown by Berenbrink et al. [4] to be Θ(log log n) with high probability for arbitrarily large m. We generalize this result to the weighted case where balls have weights drawn from an arbitrary weight distribution. We show that as long as the weight distribution has finite second moment and satisfies a mild technical condition, the gap between the weight of the heaviest bin and the weight of the average bin is independent of the number balls thrown. This is especially striking when considering heavy tailed distributions such as PowerLaw and LogNormal distributions. In these cases, as more balls are thrown, heavier and heavier weights are encountered. Nevertheless with high probability, the imbalance in the load distribution does not increase. Furthermore, if the fourth moment of the weight distribution is finite, the expected value of the gap is shown to be independent of the number of balls. 1 1
Symmetric vs. Asymmetric MultipleChoice Algorithms
"... Multiplechoice allocation algorithms have been studied intensively over the last decade. These algorithms have several applications in the areas of load balancing, routing, resource allocation and hashing. The underlying idea is simple and can be explained best in the ballsandbins model: Instead ..."
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Cited by 1 (0 self)
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Multiplechoice allocation algorithms have been studied intensively over the last decade. These algorithms have several applications in the areas of load balancing, routing, resource allocation and hashing. The underlying idea is simple and can be explained best in the ballsandbins model: Instead of assigning balls (jobs, requests, or keys) simply at random to bins (machines, servers, or positions in a hash table), choose first a small set of bins at random, inspect these bins, and place the ball into one of the bins containing the smallest number of balls among them. The simple idea of first selecting a small set of alternatives at random and then making the final choice after careful inspection of these alternatives leads to great improvements against algorithms that place their decisions simply at random. We illustrate the power of this principle in terms of simple ballsandbins processes. In particular, we study recently presented algorithms that treat bins asymmetrically in order to obtain a better load balancing. We compare the behavior of these asymmetric schemes with symmetric schemes and prove that the asymmetric schemes achieve a better load balancing than their symmetric counterparts. 1