Scheduling on Hybrid Platforms: Improved Approximability Window

TL;DR

This paper introduces a new approximation algorithm for scheduling tasks with precedence constraints on hybrid platforms with two processing unit types, improving previous bounds and approaching theoretical limits.

Contribution

The paper presents a novel $(3+2\sqrt{2})$-approximation algorithm for hybrid platform scheduling, improving upon previous algorithms and establishing a tighter approximation ratio.

Findings

Achieves an approximation ratio of $(3+2\sqrt{2})$, better than the previous 6-approximation.

Provides a conditional lower bound of 3, indicating near-optimality.

The ratio improves when the number of units of each type is similar.

Abstract

Modern platforms are using accelerators in conjunction with standard processing units in order to reduce the running time of specific operations, such as matrix operations, and improve their performance. Scheduling on such hybrid platforms is a challenging problem since the algorithms used for the case of homogeneous resources do not adapt well. In this paper we consider the problem of scheduling a set of tasks subject to precedence constraints on hybrid platforms, composed of two types of processing units. We propose a $(3+2\sqrt{2})$-approximation algorithm and a conditional lower bound of 3 on the approximation ratio. These results improve upon the 6-approximation algorithm proposed by Kedad-Sidhoum et al. as well as the lower bound of 2 due to Svensson for identical machines. Our algorithm is inspired by the former one and distinguishes the allocation and the scheduling phases. However, we propose a different allocation procedure which, although is less efficient for the allocation sub-problem, leads to an improved approximation ratio for the whole scheduling problem. This approximation ratio actually decreases when the number of processing units of each type is close and matches the conditional lower bound when they are equal.