Approximation algorithms for coupled task scheduling minimizing the sum of completion times

Abstract

AbstractIn this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several variants of this problem that are known to be $$\mathcal{N}\mathcal{P}$$ N P -hard, while also proving $$\mathcal{N}\mathcal{P}$$ N P -hardness for two variants whose complexity was unknown before. Using these results, together with constant-factor approximations for the makespan objective from the literature, we also introduce the first results on bi-objective approximation in the coupled task setting.