Efficient Multi-Processor Scheduling in Increasingly Realistic Models

TL;DR

This paper introduces advanced scheduling algorithms for computational DAGs on multi-processor systems, incorporating realistic factors like communication and synchronization costs, and demonstrates significant improvements over existing methods.

Contribution

It extends the BSP model to include NUMA effects and develops a comprehensive scheduling framework with heuristics, local search, and ILP formulations for more realistic multi-processor scheduling.

Findings

Achieves 24-44% smaller scheduling cost without NUMA effects.

Attains up to 2.5x improvement with NUMA effects.

Provides nearly 5x improvement in high communication cost scenarios.

Abstract

We study the problem of efficiently scheduling a computational DAG on multiple processors. The majority of previous works have developed and compared algorithms for this problem in relatively simple models; in contrast to this, we analyze this problem in a more realistic model that captures many real-world aspects, such as communication costs, synchronization costs, and the hierarchical structure of modern processing architectures. For this we extend the well-established BSP model of parallel computing with non-uniform memory access (NUMA) effects. We then develop a range of new scheduling algorithms to minimize the scheduling cost in this more complex setting: several initialization heuristics, a hill-climbing local search method, and several approaches that formulate (and solve) the scheduling problem as an Integer Linear Program (ILP). We combine these algorithms into a single framework, and conduct experiments on a diverse set of real-world computational DAGs to show that the resulting scheduler significantly outperforms both academic and practical baselines. In particular, even without NUMA effects, our scheduler finds solutions of 24%-44% smaller cost on average than the baselines, and in case of NUMA effects, it achieves up to a factor $2.5\times$ improvement compared to the baselines. Finally, we also develop a multilevel scheduling algorithm, which provides up to almost a factor $5\times$ improvement in the special case when the problem is dominated by very high communication costs.