An Efficient PTAS for Stochastic Load Balancing with Poisson Jobs

TL;DR

This paper presents the first efficient polynomial-time approximation scheme for stochastic load balancing with Poisson-distributed job sizes, improving previous approximation ratios and introducing new probabilistic techniques.

Contribution

It introduces the first efficient PTAS for Poisson job sizes in load balancing, with novel probabilistic methods and nearly-linear runtime in the number of jobs.

Findings

Achieved a PTAS with nearly-linear runtime in n

Improved approximation ratio from 2 to near-optimal

Developed new probabilistic results on Poisson maxima

Abstract

We give the first polynomial-time approximation scheme (PTAS) for the stochastic load balancing problem when the job sizes follow Poisson distributions. This improves upon the 2-approximation algorithm due to Goel and Indyk (FOCS'99). Moreover, our approximation scheme is an efficient PTAS that has a running time double exponential in $1/\epsilon$ but nearly-linear in $n$, where $n$ is the number of jobs and $\epsilon$ is the target error. Previously, a PTAS (not efficient) was only known for jobs that obey exponential distributions (Goel and Indyk, FOCS'99). Our algorithm relies on several probabilistic ingredients including some (seemingly) new results on scaling and the so-called "focusing effect" of maximum of Poisson random variables which might be of independent interest.