In 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 NP-hard, while also proving NP-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.
@article{arxiv.2207.00394,
title = {Approximation algorithms for coupled task scheduling minimizing the sum of completion times},
author = {David Fischer and Péter Györgyi},
journal= {arXiv preprint arXiv:2207.00394},
year = {2024}
}