Abstract: We revisit the classical non-clairvoyant problem of scheduling a set of jobs on a set of 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 the Longest Processing Time first 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, the Predicted Proportional Round Robin algorithm, 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
ACM Transactions on Parallel Computing. 2026. V.13. N1. P.1-20. DOI: 10.1145/3777410 WOS Scopus РИНЦ

Dates:

Submitted:	Oct 18, 2023
Accepted:	Nov 3, 2025
Published online:	Nov 17, 2025
Published print:	Feb 13, 2026

Identifiers:

≡ Web of science:	WOS:001704386600001
≡ Scopus:	2-s2.0-105031890281
≡ Elibrary:	87123077

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