In the paper "The complexity of mean flow time scheduling problems with release times", by Baptiste, Brucker, Chrobak, D\"urr, Kravchenko and Sourd, the authors claimed to prove strong NP-hardness of the scheduling problem P∣pmtn,rj∣∑Cj, namely multiprocessor preemptive scheduling where the objective is to minimize the mean flow time. We point out a serious error in their proof and give a new proof of strong NP-hardness for this problem.
@article{arxiv.1404.5424,
title = {A Note on NP-Hardness of Preemptive Mean Flow-Time Scheduling for Parallel Machines},
author = {Odile Bellenguez-Morineau and Marek Chrobak and Christoph Dürr and Damien Prot},
journal= {arXiv preprint arXiv:1404.5424},
year = {2014}
}