Scheduling task-trees with additive scales on parallel/distributed machines

We consider a family of jobs that are organized as a task-tree which, in particular, captures the behavior of divide-and-conquer algorithms in many typical cases (examples are QuickSort and Brute-Force Search jobs). These jobs can be described as a rooted task tree, where the cost of work at a node v in the tree is additive in the cost of v's children. We give a lower bound on the time to perform such jobs. We then provide a general algorithm that assigns these tasks to processors in a large set of parallel/distributed architectures (which includes: meshes, linear arrays, and rings). We analyze our scheme's time, showing when it is optimal or nearly optimal. We consider the cases when the tree structure is known at the node (i.e., the static case), when the division of work among children is known (the semi-dynamic case), and cases when no structure is known (i.e. fully dynamic cases).