A unified framework for designing EPTAS's for load balancing on parallel machines

TL;DR

This paper introduces a unified framework that develops an efficient EPTAS for a broad class of load balancing problems on parallel machines, encompassing various models and objectives, improving upon existing approximation schemes.

Contribution

The paper presents a general EPTAS applicable to multiple load balancing models, unifying previous approaches and enhancing approximation quality for special cases.

Findings

EPTAS applies to all previously studied special cases

Improves existing approximation schemes from PTAS to EPTAS

Handles complex objectives including makespan and $\,\ell_p$-norms with job rejection

Abstract

We consider a general load balancing problem on parallel machines. Our machine environment in particular generalizes the standard models of identical machines, and the model of uniformly related machines, as well as machines with a constant number of types, and machines with activation costs. The objective functions that we consider contain in particular the makespan objective and the minimization of the $\ell_p$-norm of the vector of loads of the machines both with possibly job rejection. We consider this general model and design an efficient polynomial time approximation scheme (EPTAS) that applies for all its previously studied special cases. This EPTAS improves the current best approximation scheme for some of these cases where only a polynomial time approximation scheme (PTAS) was known into an EPTAS.