A Note on NP-Hardness of Preemptive Mean Flow-Time Scheduling for Parallel Machines
Odile Bellenguez-Morineau, Marek Chrobak, Christoph D\"urr, Damien, Prot
TL;DR
This paper corrects a previous proof error and establishes the strong NP-hardness of preemptive mean flow-time scheduling on parallel machines, a key problem in multiprocessor scheduling.
Contribution
It provides a new, rigorous proof of strong NP-hardness for the preemptive mean flow-time scheduling problem on parallel machines.
Findings
Confirmed the NP-hardness of the problem
Provided a corrected proof of complexity
Clarified the problem's computational difficulty
Abstract
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 , 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.
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Taxonomy
TopicsScheduling and Optimization Algorithms · Advanced Manufacturing and Logistics Optimization · Optimization and Search Problems