Section: New Results

Dynamic memory-aware task-tree scheduling

Participant : Loris Marchal.

Factorizing sparse matrices using direct multifrontal methods generates directed tree-shaped task graphs, where edges represent data dependency between tasks. This work revisits the execution of tree-shaped task graphs using multiple processors that share a bounded memory. A task can only be executed if all its input and output data can fit into the memory. The key difficulty is to manage the order of the task executions so that we can achieve high parallelism while staying below the memory bound. In particular, because input data of unprocessed tasks must be kept in memory, a bad scheduling strategy might compromise the termination of the algorithm. In the single processor case, solutions that are guaranteed to be below a memory bound are known. The multi-processor case (when one tries to minimize the total completion time) has been shown to be NP-complete. We designed in this work a novel heuristic solution that has a low complexity and is guaranteed to complete the tree within a given memory bound. We compared our algorithm to state of the art strategies, and observed that on both actual execution trees and synthetic trees, we always performed better than these solutions, with average speedups between 1.25 and 1.45 on actual assembly trees. Moreover, we showed that the overhead of our algorithm is negligible even on deep trees (${10}^5$), and would allow its runtime execution.

This work is described in a technical report [39].