Abstract
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.
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Erlebach, T., Kääb, V., Möhring, R.H. (2004). Scheduling AND/OR-Networks on Identical Parallel Machines. In: Solis-Oba, R., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2003. Lecture Notes in Computer Science, vol 2909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24592-6_10
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DOI: https://doi.org/10.1007/978-3-540-24592-6_10
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