Approximation results for makespan minimization with budgeted uncertainty

Marin Bougeret 1 Klaus Jansen 2 Michael Poss 3 Lars Rohwedder 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 Theory of Parallelism
Department of Computer Science
3 MAORE - Méthodes Algorithmes pour l'Ordonnancement et les Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We study approximation algorithms for the problem of minimizing the makespan on a set of machines with uncertainty on the processing times of jobs. In the model we consider, which goes back to [3], once the schedule is defined an adversary can pick a scenario where deviation is added to some of the jobs' processing times. Given only the maximal cardinality of these jobs, and the magnitude of potential deviation for each job, the goal is to optimize the worst-case scenario. We consider both the cases of identical and unrelated machines. Our main result is an EPTAS for the case of identical machines. We also provide a 3-approximation algorithm and an inapproximability ratio of 2 − epsilon for the case of unrelated machines.
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Submitted on : Tuesday, September 3, 2019 - 3:21:15 PM
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Marin Bougeret, Klaus Jansen, Michael Poss, Lars Rohwedder. Approximation results for makespan minimization with budgeted uncertainty. WAOA 2019, Sep 2019, Munich, Germany. ⟨hal-02277357⟩

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