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Scheduling \(UET\)-tasks on a star network: complexity and approximation. (English) Zbl 1217.68039
Summary: 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.

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
Full Text: DOI
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