Compaction of Schedules and a Two-Stage Approach for Duplication-Based DAG Scheduling

Many DAG scheduling algorithms generate schedules that require prohibitively large number of processors. To address this problem, we propose a generic algorithm, SC, to minimize the processor requirement of any given valid schedule. SC preserves the schedule length of the original schedule and reduces processor count by merging processor schedules and removing redundant duplicate tasks. To the best of our knowledge, this is the first algorithm to address this highly unexplored aspect of DAG scheduling. On average, SC reduced the processor requirement 91, 82, and 72 percent for schedules generated by PLW, TCSD, and CPFD algorithms, respectively. SC algorithm has a low complexity (O{N}³) compared to most duplication-based algorithms. Moreover, it decouples processor economization from schedule length minimization problem. To take advantage of these features of SC, we also propose a scheduling algorithm SDS, having the same time complexity as SC. Our experiments demonstrate that schedules generated by SDS are only 3 percent longer than CPFD (O{N}⁴), one of the best algorithms in that respect. SDS and SC together form a two-stage scheduling algorithm that produces schedules with high quality and low processor requirement, and has lower complexity than the comparable algorithms that produce similar high-quality results.