Abstract: 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.

Cite: Bampis E. , Kononov A. , Lucarelli G. , Pascual F.
Non-Clairvoyant Makespan Minimization Scheduling with Predictions
In compilation International Symposium on Algorithms and Computation (ISAAC). 2023. – ISBN 9783959772891. DOI: 10.4230/LIPIcs.ISAAC.2023.9 Scopus OpenAlex

Dates:

Published print:	Dec 20, 2023
Published online:	Dec 20, 2023

Identifiers:

Scopus:	2-s2.0-85179131991
OpenAlex:	W4400480995

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