Balanced Allocations

Azar, Yossi; Bröder, Arndt; Karlin, Anna R.; Upfal, Eli

doi:10.1137/s0097539795288490

Cited by 592 publications

(851 citation statements)

References 10 publications

Supporting

Mentioning

843

Contrasting

Order By: Relevance

“…In particular, when n balls are thrown into n bins, it is well known that the maximum load is approximately log n/ log log n with high probability. The seminal paper of Azar, Broder, Karlin, and Upfal asked a related question: suppose the balls are placed sequentially, and each ball is placed in the least loaded of d bins chosen independently and uniformly at random [4]. In this case, they find that the maximum load is log log n/ log d + O(1) with high probability; more detailed analysis of the distribution in this case is undertaken in [10].…”

Section: Introductionmentioning

confidence: 99%

On Balls and Bins with Deletions

Cole

Frieze

Maggs

et al. 1998

Randomization and Approximation Techniques in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. We consider the problem of extending the analysis of balls and bins processes where a ball is placed in the least loaded of d randomly chosen bins to cover deletions. In particular, we are interested in the case where the system maintains a fixed load, and deletions are determined by an adversary before the process begins. We show that with high probability the load in any bin is O(log log n). In fact, this result follows from recent work by Cole et al. concerning a more difficult problem of routing in a butterfly network. The main contribution of this paper is to give a different proof of this bound, which follows the lines of the analysis of Azar, Broder, Karlin, and Upfal for the corresponding static load balancing problem. We also give a specialized (and hence simpler) version of the argument from the M. Luby, J. Rolim, and M. Serna (Eds.): RANDOM'98, LNCS 1518, pp. 145-158, 1998. © Springer-Verlag Berlin Heidelberg 1998 paper by Cole et al. for the balls and bins scenario. Finally, we provide an alternative analysis also based on the approach of Azar, Broder, Karlin, and Upfal for the special case where items are deleted according to their age. Although this analysis does not yield better bounds than our argument for the general case, it is interesting because it utilizes a twodimensional family of random variables in order to account for the age of the items. This technique may be of more general use.

show abstract

Section: Introductionmentioning

confidence: 99%

On Balls and Bins with Deletions

Cole

Frieze

Maggs

et al. 1998

Randomization and Approximation Techniques in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the maximum load we obtained a bound that is not worse than the one in the standard game [10], which is a special case of our model (all capacities set to one). For certain settings, we have been able to show that the maximum load can be even reduced to a constant by having a set of heterogeneous bins, as bigger bins are able to attract balls and help to reduce the load of smaller bins.…”

Section: Discussionmentioning

confidence: 86%

“…Lemma 1 compares the process in which m balls are allocated into n bins of total capacity C with the process that throws m balls into C unitsized bins and states that the maximum load of the former is stochastically dominated by the maximum load of the latter. By applying Theorem 1.1 of [10] on the standard game with m balls and m = C bins, we obtain a bound on the maximum load that is also valid for the first process. W.h.p., the maximum load is…”

Section: Now Lemma 2(2) Gives Usmentioning

confidence: 95%

“…The setting is similar to the evaluation of the heavily loaded case presented in [11], as having bigger, but uniform capacities with ∀c i : c i = c > 1 and throwing m = c · n balls leads to the same distribution as the classical balls-into-bins strategy, as Algorithm 1 becomes identical to the standard dchoice game presented by Azar et al [10].…”

Section: Uniform Binsmentioning

confidence: 99%

See 1 more Smart Citation

Balls into non-uniform bins

Berenbrink

Brinkmann

Friedetzky

et al. 2014

Journal of Parallel and Distributed Computing

View full text Add to dashboard Cite

Citation for published item:feren rinkD etr nd frinkm nnD endr¡ e nd priedetzkyD om nd x gelD v rs @PHIRA 9f lls into nonEuniform insF9D tourn l of p r llel nd distri uted omputingFD UR @PAF ppF PHTSEPHUTFFurther information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO• the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract Balls-into-bins games for uniform bins are widely used to model randomised load balancing strategies. Recently, balls-into-bins games have been analysed under the assumption that the selection probabilities for bins are not uniformly distributed. These new models are motivated by properties of many peer-topeer (P2P) networks. In this paper we consider scenarios in which non-uniform selection probabilities help to balance the load among the bins. While previous evaluations try to find strategies for identical bins, we investigate heterogeneous bins where the "capacities" of the bins might differ significantly. We look at the allocation of m balls into n bins of total capacity C where each ball has d random bin choices. For such heterogeneous environments we show that the maximum load remains bounded by ln ln(n)/ ln(d) + O(1) w.h.p. if the number of balls m equals the total capacity C. Further analytical and simulative results show better bounds and values for the maximum loads in special cases.

show abstract

“…There is an efficient procedure, essentially a matching algorithm for a bipartite graph, that picks one of the d bins for each player so that maximum number of balls in any bin is O(1), with probability (1−O( 1 poly(n) )). [2]. The balls and bins model is equivalent to the special case of the cake model in which all the players value the cake uniformly.…”

Section: Other Related Workmentioning

confidence: 99%