Faster approximation algorithms for scheduling with fixed jobs

Authors:
Klaus Jansen;Lars Prädel;Ulrich M. Schwarz;Ola Svensson
Affiliations:
Christian-Albrechts-Universität zu Kiel, Kiel, Germany;Christian-Albrechts-Universität zu Kiel, Kiel, Germany;Christian-Albrechts-Universität zu Kiel, Kiel, Germany;KTH Royal Institute of Technology, Stockholm, Sweden
Venue:
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
Year:
2011

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Abstract

We study the problem of scheduling jobs on identical parallel machines without preemption. In the considered setting, some of the jobs are already assigned machines and starting times, for example due to external constraints not explicitly modelled. The objective is to assign the rest of the jobs in order to minimize the makespan. It is known that this problem cannot be approximated better than within a factor of 3/2 unless P = NP. An algorithm that achieves 3/2 + ε for any ε 0 was presented by Diedrich and Jansen [DJ09], but its running time is doubly exponential in 1/ε. We present an improved algorithm with approximation ratio 3/2 and polynomial running time. We also give matching results for the related problem of scheduling with reservations. The new algorithm is both faster and conceptually simpler than the previously known algorithms.