Online scheduling of equal-length jobs: Randomization and restarts help

The input of the studied scheduling problem is a set of jobs with equal processing times, where each job is specified by its release time and deadline. The goal is to determine a single-processor, non-preemptive schedule that maximizes the number of completed jobs. In the online version, each job arrives at its release time. First, we give a barely random 5/3-competitive algorithm that uses only one random bit; we also show a lower bound of 3/2 for barely random algorithms that choose one of two deterministic algorithms. Second, we give a deterministic 3/2-competitive algorithm in the model that allows restarts, and we show that in this model the ratio 3/2 is optimal.