Scheduling \(UET\)-tasks on a star network: complexity and approximation.

*(English)*Zbl 1217.68039Summary: 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.

##### MSC:

68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |

68Q17 | Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) |

68W25 | Approximation algorithms |

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\textit{R. Giroudeau} et al., 4OR 9, No. 1, 29--48, erratum 111 (2011; Zbl 1217.68039)

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