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

TL;DR

This paper develops approximation algorithms for coupled task scheduling problems aiming to minimize total completion time, addressing NP-hard variants and introducing bi-objective approximation results.

Contribution

It provides the first constant-factor approximation algorithms for several NP-hard variants and proves NP-hardness for previously unknown cases, also exploring bi-objective approximations.

Findings

Constant-factor approximation algorithms for NP-hard variants.

NP-hardness proofs for two previously unclassified variants.

First bi-objective approximation results in coupled task scheduling.

Abstract

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.