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Author Vcking, Berthold
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2003
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Randomized algorithms ♦ Balls and bins processes ♦ Probabilistic analysis
Abstract This article deals with randomized allocation processes placing sequentially $\textit{n}$ balls into $\textit{n}$ bins. We consider multiple-choice algorithms that choose $\textit{d}$ locations (bins) for each ball at random, inspect the content of these locations, and then place the ball into one of them, for example, in a location with minimum number of balls. The goal is to achieve a good load balancing. This objective is measured in terms of the maximum load, that is, the maximum number of balls in the same bin.Multiple-choice algorithms have been studied extensively in the past. Previous analyses typically assume that the $\textit{d}$ locations for each ball are drawn uniformly and independently from the set of all bins. We investigate whether a nonuniform or dependent selection of the $\textit{d}$ locations of a ball may lead to a better load balancing. Three types of selection, resulting in three classes of algorithms, are distinguished: (1) uniform and independent, (2) nonuniform and independent, and (3) nonuniform and dependent.Our first result shows that the well-studied uniform greedy algorithm (class 1) does not obtain the smallest possible maximum load. In particular, we introduce a nonuniform algorithm (class 2) that obtains a better load balancing. Surprisingly, this algorithm uses an unfair tie-breaking mechanism, called Always-Go-Left, resulting in an asymmetric assignment of the balls to the bins. Our second result is a lower bound showing that a dependent allocation (class 3) cannot yield significant further improvement.Our upper and lower bounds on the maximum load are tight up to additive constants, proving that the Always-Go-Left algorithm achieves an almost optimal load balancing among all sequential multiple-choice algorithm. Furthermore, we show that the results for the Always-Go-Left algorithm can be generalized to allocation processes with more balls than bins and even to infinite processes in which balls are inserted and deleted by an oblivious adversary.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2003-07-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 50
Issue Number 4
Page Count 22
Starting Page 568
Ending Page 589


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Source: ACM Digital Library