EPTAS for parallel identical machine scheduling with time restrictions

TL;DR

This paper presents an Efficient Polynomial-Time Approximation Scheme (EPTAS) for scheduling identical machines with time restrictions, improving upon previous results limited to single machines or constant B values.

Contribution

We develop the first EPTAS for parallel identical machine scheduling with variable B, extending the scope beyond prior PTAS results for single machines.

Findings

EPTAS achieves near-optimal makespan within any desired approximation ratio.

The scheme generalizes previous PTAS results to multiple machines and variable B.

This advances the theoretical understanding of complex scheduling problems.

Abstract

We consider the non-preemptive scheduling problem on identical machines where there is a parameter B and each machine in every unit length time interval can process up to B different jobs. The goal function we consider is the makespan minimization and we develop an EPTAS for this problem. Prior to our work a PTAS was known only for the case of one machine and constant values of B, and even the case of non-constant values of B on one machine was not known to admit a PTAS.