Abstract
In this article we investigate complexity and approximation on a processor network where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no polynomial-time heuristic with a performance guarantee smaller than \({\frac{6}{5}}\) (respectively \({\frac{14}{13}}\)) for minimization of the makespan (respectively the total job completion time) on a processor network represented by a star. Moreover, we design an efficient polynomial-time approximation algorithm with a worst-case ratio of four. We also prove that a polynomial-time algorithm exists for a schedule with a length of at most four. Lastly, we generalize all previous results on complexity and approximation.
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An erratum to this article can be found at http://dx.doi.org/10.1007/s10288-011-0163-y
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Giroudeau, R., König, J.C. & Valery, B. Scheduling UET-tasks on a star network: complexity and approximation. 4OR-Q J Oper Res 9, 29–48 (2011). https://doi.org/10.1007/s10288-010-0127-7
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DOI: https://doi.org/10.1007/s10288-010-0127-7