Empowering the Configuration-IP $-$ New PTAS Results for Scheduling with Setups Times
Klaus Jansen, Kim-Manuel Klein, Marten Maack, Malin Rau

TL;DR
This paper introduces a new module configuration integer linear programming approach, enabling efficient approximation schemes for complex scheduling problems with setup times, significantly improving over previous constant factor approximations.
Contribution
The authors develop an augmented configuration IP within n-fold integer programming, providing the first EPTAS for scheduling with setup times, including parallel and non-splittable job variants.
Findings
EPTAS with single exponential time for parallel jobs
Double exponential time EPTAS for non-parallel jobs
Improved approximation ratios from previous constant factors
Abstract
Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems, where a set of items has to be placed in multiple target locations. Herein a configuration describes a possible placement on one of the target locations, and the IP is used to chose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and therefore be solved efficiently. As an application, we consider scheduling problems with setup times, in which a set of jobs has to be scheduled on a set of identical machines, with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be…
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