Balls into non-uniform bins

Abstract

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.

Converting Online Algorithms to Local Computation Algorithms

“…Previously, Alon et al [2] show that the expected size of the query tree is constant, and O(log d+1 n) w.h.p. 5 Our improvement is significant in removing the dependence on d from the exponent of the logarithm. We also show that when the degrees of the graph are distributed binomially, we can achieve the same bound on the size of the query tree.…”

“…Corollary 6. (Using [5]) Suppose we wish to allocate m balls into n ≤ m bins, where each bin i has a capacity c i , and i c i = m. Assume that the size of a large bin is at least rn log n, for large enough r. Suppose we have s small bins with total capacity m s , and that m s = O((n log n) 2/3 ). There exists a (log n, log n, 1/n) LCA which allocates the balls in such a way that the expected maximum load is less than 5.…”

Stochastic Coordination in Heterogeneous Load Balancing Systems

“…A related line of work dealing with load balancing challenges in distributed systems is based on the balls-into-bins model [1], including extensions to dynamic or heterogeneous settings (e.g., [4,6]). In the balls-into-bins model, it is commonly possible to obtain more precise theoretical guarantees.…”

Online Distributed User Association for Heterogeneous Radio Access Network

“…A solution to balls into non-uniform bins was investigated in Ref. [47], where a heterogeneous environment was considered and the balls are assigned to the bins. After the allocation, the maximum load (number of balls) was found to be lnln(n)ln(d), where n is the number of bins and d is the number of choices for a ball.…”

“…Authors in Ref. [47] proposed a “balls into non-uniform bins” method. Accordingly, we first reduced our BS selection problem to the “balls into non-uniform” problem, and then applied the algorithm prescribed therein.…”