Probabilistic performance analysis of scheduling parallel tasks with precedence constraints on mesh connected multicomputers

We investigate the problem of scheduling parallel tasks with precedence constraints on mesh connected multicomputers. It is an open problem as to whether there exists an approximation algorithm that has a finite worst-case performance ratio. We propose a simple level scheduling algorithm LL as a first attempt to solve our problem. There are three basic techniques in algorithm LL, i.e., a layer by layer scheduling strategy to handle precedence constraints, the largest-job-first algorithm to schedule tasks in the same layer, and the two dimensional buddy system for system partitioning. Algorithm LL does not have a finite worst-case performance ratio. However, its average-case performance ratio is quite acceptable. It is shown that for wide task graphs and typical task size distributions, the asymptotic average-case performance ratio of algorithm LL is about two for all probability distributions of task execution times.