Approximating coupled-task scheduling problems with equal exact delays

Abstract

We consider a coupled-task single machine scheduling problem with equal exact delays and makespan as the objective function. We design a 3-approximation algorithm for the general case of this problem. We also prove that the existence of a (1.25−ε)-approximation algorithm implies P=NP. The inapproximability result remains valid for the case when the processing times of the two operations of each job are equal. We prove that this case is approximable within a factor of 1.5.