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Scheduling AND/OR-Networks on Identical Parallel Machines

Kääb, Vanessa; Erlebach, Thomas; Möhring, Rolf H.

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

Scheduling precedence constrained jobs on identical parallel machines is a well investigated problem with many applications. AND/OR-networks constitute a useful generalization of standard precedence constraints where certain jobs can be executed as soon as at least one of their direct predecessors is completed. For the problem of scheduling AND/OR-networks on parallel machines, we present a 2-approximation algorithm for the objective of minimizing the makespan. The main idea of the algorithm is to transform the AND/OR constraints into standard constraints. For the objective of minimizing the total weighted completion time on one machine, scheduling AND/OR-networks is as hard to approximate as Label Cover. We show that list scheduling with shortest processing time rule is an O(sqrt(n))-approximation for unit weights on one machine and an n-approximation for arbitrary weights.