Empowering the Configuration-IP - New PTAS Results for Scheduling with Setups Times
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 processed an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time f(1/epsilon) x poly(|I|) with a single exponential term in f for the first and a double exponential one for the second case. Previously, only constant factor approximations of 5/3 and 4/3 + epsilon respectively were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine.
Parallel Machines
Setup Time
EPTAS
n-fold integer programming
Theory of computation~Scheduling algorithms
Theory of computation~Discrete optimization
44:1-44:19
Regular Paper
The long version is hosted on arXiv [Klaus Jansen et al., 2018], https://arxiv.org/abs/1801.06460.
Klaus
Jansen
Klaus Jansen
Department of Computer Science, Kiel University, Kiel, Germany
German Research Foundation (DFG) project JA 612/20-1
Kim-Manuel
Klein
Kim-Manuel Klein
Department of Computer Science, Kiel University, Kiel, Germany
Marten
Maack
Marten Maack
Department of Computer Science, Kiel University, Kiel, Germany
Malin
Rau
Malin Rau
Department of Computer Science, Kiel University, Kiel, Germany
10.4230/LIPIcs.ITCS.2019.44
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Klaus Jansen, Kim-Manuel Klein, Marten Maack, and Malin Rau
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