Affiliation:
1. LIP, ENS Lyon, France
2. University of Kansas, USA
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 the 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.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Computer Science Applications,Hardware and Architecture,Modeling and Simulation,Software
Reference33 articles.
1. Kunal Agrawal Charles E. Leiserson and Jim Sukha. 2010. Executing task graphs using work-stealing. In IPDPS. 1–12. Kunal Agrawal Charles E. Leiserson and Jim Sukha. 2010. Executing task graphs using work-stealing. In IPDPS. 1–12.
2. Gene M. Amdahl. 1967. Validity of the Single Processor Approach to Achieving Large Scale Computing Capabilities. In AFIPS’67. 483–485. Gene M. Amdahl. 1967. Validity of the Single Processor Approach to Achieving Large Scale Computing Capabilities. In AFIPS’67. 483–485.
3. Krishna P. Belkhale and Prithviraj Banerjee . 1990 . An Approximate Algorithm for the Partitionable Independent Task Scheduling Problem. In ICPP. 72–75. Krishna P. Belkhale and Prithviraj Banerjee. 1990. An Approximate Algorithm for the Partitionable Independent Task Scheduling Problem. In ICPP. 72–75.
4. Krishna P. Belkhale Prithviraj Banerjee and W. Springfield Av. 1991. A Scheduling Algorithm for Parallelizable Dependent Tasks. In IPPS. 500–506. Krishna P. Belkhale Prithviraj Banerjee and W. Springfield Av. 1991. A Scheduling Algorithm for Parallelizable Dependent Tasks. In IPPS. 500–506.
5. Anne Benoit , Valentin Le Fèvre , Lucas Perotin, Padma Raghavan, Yves Robert, and Hongyang Sun. 2020 . Resilient scheduling of moldable jobs on failure-prone platforms. In IEEE Cluster . Anne Benoit, Valentin Le Fèvre, Lucas Perotin, Padma Raghavan, Yves Robert, and Hongyang Sun. 2020. Resilient scheduling of moldable jobs on failure-prone platforms. In IEEE Cluster.