Malleable task-graph scheduling with a practical speed-up model

Loris Marchal (1, 2) , Bertrand Simon (1, 2) , Oliver Sinnen (3) , Frédéric Vivien (1, 2)

1 ROMA - Optimisation des ressources : modèles, algorithmes et ordonnancement
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 ECE - Department of Electrical and Computer Engineering [Auckland ]

Scientific workloads are often described by Directed Acyclic task Graphs. Indeed, DAGs represent both a theoretical model and the structure employed by dynamic runtime schedulers to handle HPC applications. A natural problem is then to compute a makespan-minimizing schedule of a given graph. In this paper, we are motivated by task graphs arising from multifrontal factorizations of sparse matrices and therefore work under the following practical model. Tasks are malleable (i.e., a single task can be allotted a time-varying number of processors) and their speedup behaves perfectly up to a first threshold, then speedup increases linearly, but not perfectly, up to a second threshold where the speedup levels off and remains constant. After proving the NP-hardness of minimizing the makespan of DAGs under this model, we study several heuristics. We propose model-optimized variants for PROPSCHEDULING, widely used in linear algebra application scheduling, and FLOWFLEX. GREEDYFILLING is proposed, a novel heuristic designed for our speedup model, and we demonstrate that PROPSCHEDULING and GREEDYFILLING are 2-approximation algorithms. In the evaluation, employing synthetic data sets and task graphs arising from multifrontal factorization, the proposed optimized variants and GREEDYFILLING significantly outperform the traditional algorithms, whereby GREEDYFILLING demonstrates a particular strength for balanced graphs.

Keywords: speedup model; approximation algorithms; proportional mapping; Scheduling; task graph; malleable tasks

Domains: Distributed, Parallel, and Cluster Computing [cs.DC]; Data Structures and Algorithms [cs.DS]

Loris Marchal, Bertrand Simon, Oliver Sinnen, Frédéric Vivien. Malleable task-graph scheduling with a practical speed-up model. IEEE Transactions on Parallel and Distributed Systems, 2018, 29 (6), pp.1357-1370. ⟨10.1109/TPDS.2018.2793886⟩. ⟨hal-01687189⟩