Multiprocessor Scheduling with Memory Constraints: Fundamental Properties and Finding Optimal Solutions

TL;DR

This paper investigates the complex problem of scheduling computational tasks on multiprocessors with limited memory, analyzing its theoretical properties, computational complexity, and proposing an ILP-based algorithm that outperforms traditional methods.

Contribution

It introduces a comprehensive analysis of the problem's fundamental properties and develops an ILP-based scheduling algorithm that improves solution quality over existing approaches.

Findings

ILP-based scheduling yields better solutions than classical methods.

The problem's complexity is characterized, showing the difficulty of joint optimization.

Separately optimizing parallelization and memory management can be significantly suboptimal.

Abstract

We study the problem of scheduling a general computational DAG on multiple processors in a 2-level memory hierarchy. This setting is a natural generalization of several prominent models in the literature, and it simultaneously captures workload balancing, communication, and data movement due to cache size limitations. We first analyze the fundamental properties of this problem from a theoretical perspective, such as its computational complexity. We also prove that optimizing parallelization and memory management separately, as done in many applications, can result in a solution that is a linear factor away from the optimum. On the algorithmic side, we discuss a natural technique to represent and solve the problem as an Integer Linear Program (ILP). We develop a holistic scheduling algorithm based on this approach, and we experimentally study its performance and properties on a small benchmark of computational tasks. Our results confirm that the ILP-based method can indeed find considerably better solutions than a baseline which combines classical scheduling algorithms and memory management policies.