Online Makespan Minimization with Budgeted Uncertainty - Albers, Susanne; Janke, Maximilian (Algorithms and Data Structures, 2021)
We study Online Makespan Minimization with uncertain job processing times. Jobs are assigned to m parallel and identical machines. Preemption is not allowed. Each job has a regular processing time while up to Γ $$\varGamma $$ jobs fail and require additional processing time. The goal is to minimize the makespan, the time it takes to process all jobs if these Γ $$\varGamma $$ failing jobs are chosen worst possible. This models real-world applications where acts of nature beyond control have to be accounted for. So far Makespan Minimization With Budgeted Uncertainty has only been studied as an offline problem. We are first to provide a comprehensive analysis of the corresponding online problem. We provide a lower bound of 2 for general deterministic algorithms showing that the problem is more difficult than its special case, classical Online Makespan Minimization. We further analyze Graham’s Greedy strategy and show that it is precisely 3-2m $$\left( 3-\frac{2}{m}\right) $$ -competitive. This bound is tight. We finally provide a more sophisticated deterministic algorithm whose competitive ratio approaches 2.9052.