This talk addresses the challenges of online scheduling within high-performance computing (HPC) systems, focusing on rigid parallel tasks with precedence constraints organized as a directed acyclic graph (DAG). We introduce an online algorithm, called CatBatch, which efficiently schedules tasks to minimize the overall completion time, or the makespan. Although CatBatch only discovers tasks on the fly when they are ready, its competitive ratio almost matches the best offline algorithm, and is proven to be near-optimal.