Optimality of HLF for scheduling divide-and-conquer UET task graphs on identical parallel processors

The problem of scheduling a set of nn unit execution time (UET) tasks subject to precedence constraints on mm identical parallel processors is known to be NPNP-hard in the strong sense. However, polynomial time algorithms exist for some classes of precedence graphs. In this paper, we consider a class of divide-and-conquer graphs that naturally models the execution of the recursive control abstraction of divide-and-conquer algorithms. We prove that the Highest Level First (HLF) strategy minimizes the schedule length for this class, thus settling a conjecture of Rayward-Smith and Clark.