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Scheduling in the presence of processor networks : complexity and approximation. (English. French summary) Zbl 1242.90075
Summary: We study the problem of makespan minimization for the multiprocessor scheduling problem in the presence of communication delays. The communication delay between two tasks $$i$$ and $$j$$ depends on the distance between the two processors on which these two tasks are executed. Lahlou shows that a simple polynomial-time algorithm exists when the length of the schedule is at most two (the problem becomes $$\mathcal {NP}$$-complete when the length of the schedule is at most three). We prove that there is no polynomial-time algorithm with a performance guarantee of less than 4/3 (unless $$\mathcal P = \mathcal {NP})$$ to minimize the makespan when the network topology is a chain or ring and the precedence graph is a bipartite graph of depth one. We also develop two polynomial-time approximation algorithms with constant ratio dedicated to cases where the processor network admits a limited or unlimited number of processors.
##### MSC:
 90B35 Deterministic scheduling theory in operations research 68W25 Approximation algorithms 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
##### Keywords:
scheduling; non-approximability; processor network model
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##### References:
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