Balanced Allocations: The Heavily Loaded Case

Berenbrink, Petra; Czumaj, Artur; Steger, Angelika; Vöcking, Berthold

doi:10.1137/s009753970444435x

Cited by 161 publications

(275 citation statements)

References 11 publications

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“…However, if the number of choices d is allowed to (slowly) grow with the deviation in the probability distribution, the maximum load is again bounded by m n + O(ln ln(n)) (which complies with [11]). The presented bounds are tight in a way that a smaller d leads to a deviation of the load linear in m.…”

Section: Introductionsupporting

confidence: 53%

Balls into non-uniform bins

Berenbrink

Brinkmann

Friedetzky

et al. 2014

Journal of Parallel and Distributed Computing

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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.

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Section: Introductionsupporting

confidence: 53%

Balls into non-uniform bins

Berenbrink

Brinkmann

Friedetzky

et al. 2014

Journal of Parallel and Distributed Computing

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“…Balls-into-bins processes have been extensively studied in the area of parallel and distributed computing, mainly to address balanced-allocation problems [19][20][21], PRAM simulation [22] and hashing [23]. In order to optimize the total number of random bin choices used for the allocation, further allocation strategies have been proposed and analyzed (see, e.g., [24][25][26][27][28]).…”

Section: Related Workmentioning

confidence: 99%

Self-stabilizing repeated balls-into-bins

et al. 2017

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We study the following synchronous process that we call repeated balls-into-bins. The process is started by assigning n balls to n bins in an arbitrary fashion. In every subsequent round, one ball is extracted from each non-empty bin according to some fixed strategy (random, FIFO, etc), and re-assigned to one of the n bins uniformly at random. We define a configuration legitimate if its maximum load is O(log n). We prove that, starting from any configuration, the process converges to a legitimate configuration in linear time and then only takes on legitimate configurations over a period of length bounded by any polynomial in n, with high probability (w.h.p.). This implies that the process is self-stabilizing and that every ball traverses all bins within O(n log 2 n) rounds, w.h.p.

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“…Wieder [12] demonstrates that in the scenario of Byers et al the maximum difference between the loads grows with m. Thus, for m ≫ n the bounds are not as tight as in the standard case [11]. However, if the number of choices d is allowed to (slowly) grow with the deviation in the probability distribution, the maximum load is again bounded by m n + O(ln ln(n)) (which complies with [11]).…”

Section: Introductionmentioning

confidence: 83%

Balls into non-uniform bins

Berenbrink

Brinkmann

Friedetzky

et al. 2010

2010 IEEE International Symposium on Parallel &Amp; Distributed Processing (IPDPS)

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Citation for published item:ferenrinkD etr nd frinkmnnD endr¡ e nd priedetzkyD om nd xgelD vrs @PHIRA 9flls into nonEuniform insF9D tournl of prllel nd distriuted omputingFD UR @PAF ppF PHTSEPHUTF Further 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-prot 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

Balanced Allocations: The Heavily Loaded Case

Cited by 161 publications

References 11 publications

Balls into non-uniform bins

Balls into non-uniform bins

Self-stabilizing repeated balls-into-bins

Balls into non-uniform bins

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