The 1-2-3-Toolkit for Building Your Own Balls-into-Bins Algorithm

TL;DR

This paper introduces a flexible toolkit for designing and analyzing distributed balls-into-bins algorithms, leveraging concentration bounds and ranking mechanisms to improve load balancing efficiency.

Contribution

It presents a novel iterative estimation method and ranking-based algorithm classification, enhancing initial bin commitment and providing accurate load distribution predictions.

Findings

Ranking mechanism improves first-round ball commitments

Simulation results confirm high accuracy for large-scale scenarios

Method provides precise load estimates after each round

Abstract

In this work, we examine a generic class of simple distributed balls-into-bins algorithms. Exploiting the strong concentration bounds that apply to balls-into-bins games, we provide an iterative method to compute accurate estimates of the remaining balls and the load distribution after each round. Each algorithm is classified by (i) the load that bins accept in a given round, (ii) the number of messages each ball sends in a given round, and (iii) whether each such message is given a rank expressing the sender's inclination to commit to the receiving bin (if feasible). This novel ranking mechanism results in notable improvements, in particular in the number of balls that may commit to a bin in the first round of the algorithm. Simulations independently verify the correctness of the results and confirm that our approximation is highly accurate even for a moderate number of $10^6$ balls and bins.