Scheduling Trees of Malleable Tasks for Sparse Linear Algebra
Abdou Guermouche, Loris Marchal, Bertrand Simon, Fr\'ed\'eric, Vivien

TL;DR
This paper investigates optimal scheduling of malleable tasks structured as trees in sparse linear algebra, providing new theoretical insights, approximation algorithms, and demonstrating up to 16% performance gains in simulations.
Contribution
It introduces simplified proofs for optimal task allocation, extends the model to distributed platforms, proves NP-completeness, and offers algorithms with practical performance improvements.
Findings
Optimal control-based scheduling solutions for malleable tasks
NP-completeness of distributed task scheduling
Up to 16% performance improvement in simulations
Abstract
Scientific workloads are often described as directed acyclic task graphs. In this paper, we focus on the multifrontal factorization of sparse matrices, whose task graph is structured as a tree of parallel tasks. Among the existing models for parallel tasks, the concept of malleable tasks is especially powerful as it allows each task to be processed on a time-varying number of processors. Following the model advocated by Prasanna and Musicus for matrix computations, we consider malleable tasks whose speedup is , where is the fractional share of processors on which a task executes, and () is a parameter which does not depend on the task. We first motivate the relevance of this model for our application with actual experiments on multicore platforms. Then, we study the optimal allocation proposed by Prasanna and Musicus for makespan minimization…
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