Probabilistic Analysis of Scheduling Precedence Constrained Parallel Tasks on Multicomputers with Contiguous Processor Allocation

ÐGiven a set of precedence constrained parallel tasks with their processor requirements and execution times, the problem of scheduling precedence constrained parallel tasks on multicomputers with contiguous processor allocation is to find a nonpreemptive schedule of the tasks on a multicomputer such that the schedule length is minimized. This scheduling problem is substantially more difficult than other scheduling problems due to precedence constraints among tasks, the inherent difficulty of task scheduling, and processor allocation in multicomputers. We present an approximation algorithm called LLB that schedules tasks level-by-level using the largest-task-first strategy supported by the binary system partitioning scheme to handle the three difficult issues in our scheduling problem. Though algorithm LLB does not have a bounded worst-case performance ratio, we show through probabilistic analysis that LLB has a quite reasonable average-case performance ratio for typical classes of parallel computations. In particular, algorithm LLB has an average-case performance ratio less than two for large scale parallel computations that have wide task graphs (i.e., that exhibit large parallelism). Index TermsÐAverage-case performance ratio, binary system partitioning, contiguous processor allocation, largest-task-first, parallel task, precedence constraint, probabilistic analysis, task scheduling.