Model and complexity results for tree traversals on hybrid platforms

Abstract

We study the complexity of traversing tree-shaped workflows whose tasks require large I/O files. We target a heterogeneous architecture with two resources of different types, each equipped with its own memory, such as a multicore node equipped with a dedicated accelerator (FPGA or GPU). Tasks in the workflow are tagged with the type of resource that is needed for their processing. Besides, a task can be processed on a given resource only if all its input files and output files can be stored in the corresponding memory. At a given execution step, the amount of data stored in each memory strongly depends upon the ordering in which the tasks are executed, and upon when communications between both memories are scheduled. The objective is to determine an efficient traversal that minimizes the maximum amount of memory of each type needed to traverse the whole tree. In this paper, we establish the complexity of this two-memory scheduling problem, provide inapproximability results, and show how to determine the optimal depth-first traversal. Altogether, these results lay the foundations for memory-aware scheduling algorithms on heterogeneous platforms. © 2013 Springer-Verlag.