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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.

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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