Non-Clairvoyant Makespan Minimization Scheduling with Predictions

Authors Evripidis Bampis , Alexander Kononov , Giorgio Lucarelli , Fanny Pascual

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Evripidis Bampis
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
Alexander Kononov
  • Sobolev Institute of Mathematics, Novosibirsk, Russia
  • Novosibirsk State University, Russia
Giorgio Lucarelli
  • LCOMS, University of Lorraine, Metz, France
Fanny Pascual
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France

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Evripidis Bampis, Alexander Kononov, Giorgio Lucarelli, and Fanny Pascual. Non-Clairvoyant Makespan Minimization Scheduling with Predictions. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We revisit the classical non-clairvoyant problem of scheduling a set of n jobs on a set of m parallel identical machines where the processing time of a job is not known until the job finishes. Our objective is the minimization of the makespan, i.e., the date at which the last job terminates its execution. We adopt the framework of learning-augmented algorithms and we study the question of whether (possibly erroneous) predictions may help design algorithms with a competitive ratio which is good when the prediction is accurate (consistency), deteriorates gradually with respect to the prediction error (smoothness), and not too bad and bounded when the prediction is arbitrarily bad (robustness). We first consider the non-preemptive case and we devise lower bounds, as a function of the error of the prediction, for any deterministic learning-augmented algorithm. Then we analyze a variant of Longest Processing Time first (LPT) algorithm (with and without release dates) and we prove that it is consistent, smooth, and robust. Furthermore, we study the preemptive case and we provide lower bounds for any deterministic algorithm with predictions as a function of the prediction error. Finally, we introduce a variant of the classical Round Robin algorithm (RR), the Predicted Proportional Round Robin algorithm (PPRR), which we prove to be consistent, smooth and robust.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • scheduling
  • online
  • learning-augmented algorithm


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