Improved Online Scheduling of Moldable Task Graphs under Common Speedup Models

TL;DR

This paper introduces a new online scheduling algorithm for moldable task graphs on multiprocessors, achieving constant competitive ratios under various speedup models, and establishes lower bounds for algorithm competitiveness.

Contribution

The paper presents a novel online scheduling algorithm with proven competitive ratios for multiple speedup models and provides matching lower bounds, advancing the understanding of moldable task graph scheduling.

Findings

Achieves constant competitive ratios under roofline, communication, and Amdahl models.

Provides lower bounds matching the algorithm's ratios for several models.

Establishes non-constant lower bounds depending on task graph length for arbitrary models.

Abstract

We consider the online scheduling problem of moldable task graphs on multiprocessor systems for minimizing the overall completion time (or makespan). Moldable job scheduling has been widely studied in the literature, 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 scheduling algorithm for this problem and derive constant competitive ratios under several common yet realistic speedup models (i.e., roofline, communication, Amdahl, and a general combination). These results improve the ones we have shown in the preliminary version of this paper. We also prove, for each speedup model, a lower bound on the competitiveness of any online list scheduling algorithm that allocates processors to a task based only on the task's parameters and not on its position in the graph. This lower bound matches exactly the competitive ratio of our algorithm for the roofline, communication and Amdahl's model, and is close to the ratio for the general model. Finally, we provide a 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.