Tighter Bounds on Non-clairvoyant Parallel Machine Scheduling with Prediction to Minimize Makespan

TL;DR

This work analyzes non-clairvoyant parallel machine scheduling with prediction on $m$ identical machines, introducing prediction error $\alpha=\max_j\{p_j/q_j, q_j/p_j\}$ and aiming to minimize makespan. It provides improved lower bounds and tighter competitive ratios for both non-preemptive and preemptive settings, expressed as explicit functions of $\alpha$, and evaluates two prediction-aware algorithms: LPPT for non-preemptive and PPRR for preemptive scheduling. Key contributions include refined lower bounds, calibrated upper bounds (including exact results for small $m$), and optimality conditions tied to $\alpha$, demonstrating that predictive information can meaningfully improve performance. Collectively, the results guide the design of prediction-informed online schedulers on identical machines and quantify the gains achievable as predictions become more accurate.

Abstract

This paper investigates the non-clairvoyant parallel machine scheduling problem with prediction, with the objective of minimizing the makespan. Improved lower bounds for the problem and competitive ratios of online algorithms with respect to the prediction error are presented for both the non-preemptive and preemptive cases on m identical machines.

Theorems & Definitions (6)

• Theorem 2.1
• Theorem 2.2
• Theorem 2.3
• Theorem 2.4
• Theorem 3.1
• Theorem 3.2