Scheduling Fork-Join Task Graphs with Communication Delays and Equal Processing Times

Task scheduling for parallel computing is strongly NP-hard even without precedence constraints P||Cmax. With any kind of precedence constraints and communication delays the problem becomes less manageable still. We look at the specific case of scheduling under the precedence constraints of a fork-join structure (including communication delays) P|fork − join, cij|Cmax. This represents any kind of computation that divides into sub-computations with the end results being processed together, such as divide and conquer. This kind of computation is fundamental. We look at the instances where some of the computation and communication costs are constant, present polynomial time algorithms for them, and explore the boundary between tractability and NP-hardness around this problem.