Scheduling AND/OR-networks on identical parallel machines

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 make-span. 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(rootn)-approximation for unit weights on one machine and an n-approximation for arbitrary weights.