The multiprocessor scheduling of precedence-constrained task systems in the presence of interprocessor communication delays

The problem of scheduling precedence-constrained task systems characterized by interprocessor communication delays is addressed. It is assumed that task duplication is permitted. The target machine is a homogeneous multiprocessor with an unbounded number of processors. The general problem is known to be NP-hard; however, when communication delays are small relative to task execution times, the C.P.M. based approach of Colin and Chrétienne (1991) yields an optimal schedule in polynomial time. Extensions to this method of Colin and Chrétienne are presented here, which allow for polynomial-time optimal schedule generation for certain categories of task systems with arbitrary precedence relations, processing times, and communication delays.