Abstract
We investigate the problem of minimizing the makespan for the multiprocessor scheduling problem. We show that there is no hope of finding a ρ-approximation with \(\displaystyle \rho < 1+ 1/(c+4)\) (unless \({\cal{P}}={\cal{NP}}\)) for the case where all the tasks of the precedence graph have unit execution times, where the multiprocessor is composed of an unrestricted number of machines, and where c denotes the communication delay between two tasks i and j submitted to a precedence constraint and to be processed by two different machines. The problem becomes polynomial whenever the makespan is at the most (c+1). The (c+2) case is still partially opened.
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Giroudeau, R., König, J.C., Moulaï, F.K., Palaysi, J. (2005). Complexity and Approximation for the Precedence Constrained Scheduling Problem with Large Communication Delays. In: Cunha, J.C., Medeiros, P.D. (eds) Euro-Par 2005 Parallel Processing. Euro-Par 2005. Lecture Notes in Computer Science, vol 3648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549468_30
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DOI: https://doi.org/10.1007/11549468_30
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