Scheduling moldable tasks on homogeneous multi-cluster platforms with GPUs

This paper examines task scheduling in homogeneous multi-cluster platforms, equipped with Graphics Processing Units (GPUs), with the aim of minimizing the makespan. We assume that tasks can be parallelized across these platforms under the moldable model. Recognizing the NP-hard nature of the problem, our goal is to develop algorithms that provide approximation ratios. While existing research has established algorithms for single-cluster GPU environments, scaling these to multi-cluster platforms introduces new challenges, especially due to the restriction that tasks cannot use processors from different clusters. We propose an integer programming-based algorithm that achieves an approximation ratio of $\frac{3}{2}+ϵ$, trading off runtime for an improved approximation ratio. Additionally, leveraging recent theoretical advancements, we have created a polynomial-time algorithm with an approximation ratio of $2+ϵ$. Empirical computational experiments show that our algorithms surpass their counterparts in empirical approximation ratios.