Balls into non-uniform bins

Abstract

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.

Local Computation Mechanism Design

“…The proof is similar to the proof for the unmodified Greedy algorithm in the case of non-uniform bins of [BBFN14]. We provide it in Appendix A for completeness.…”

“…The standard setting (cf. [BBFN14,Wie07]) is a slight variation on the basic power-of-d choices setting proposed in [ABKU99], for some constant d ≥ 2. For each job j, the mechanism chooses a subset M j ⊆ M, |M j | = d of machines that the job can be allocated to.…”

Local computation mechanism design

“…We therefore need to show a payment scheme which can be implemented in an LCA and guarantees truthfulness. Our payment schemes are similar in idea to the payments schemes of [APTT03] and [BBFN14].…”

Parallel Load Balancing on constrained client-server topologies

“…This natural extension of previous work is inspired by possible network applications where: i) based on previous experiences, a client (a server) may decide to send (accept) the requests only to (from) a fixed subset of trusted servers (clients) and/or ii) clients and servers are placed over a metric space so that only non-random client-servers interactions turn out to be feasible because of proximity constraints. Such possible scenarios motivated previous important studies on sequential Load Balancing algorithms [8][9][10]. To the best of our knowledge, efficient solutions for non-dense graphs are in fact available only for the classic sequential model.…”