Online Scheduling of Moldable Task Graphs under Common Speedup Models

The problem of scheduling moldable tasks on multiprocessor systems with the objective of minimizing the overall completion time (or makespan) has been widely studied, in particular when tasks have dependencies (i.e., task graphs), or when tasks are released on-the-fly (i.e., online). However, few studies have focused on both (i.e., online scheduling of moldable task graphs). In this paper, we design a new online algorithm and derive constant competitive ratios for this problem under several common yet realistic speedup models (i.e., roofline, communication, Amdahl, and a general combination). We also prove, for each model, a lower bound on the competitiveness of our algorithm, which is very close to the constant competitive ratio. Finally, we provide the first lower bound on the competitive ratio of any deterministic online algorithm for the arbitrary speedup model, which is not constant but depends on the number of tasks in the longest path of the graph.