Structural Parameters for Scheduling with Assignment Restrictions

We consider scheduling on identical and unrelated parallel machines with job assignment restrictions. These problems are NP-hard and they do not admit polynomial time approximation algorithms with approximation ratios smaller than 1.5 unless P=NP. However, if we impose limitations on the set of machines that can process a job, the problem sometimes becomes easier in the sense that algorithms with approximation ratios better than 1.5 exist. We introduce three graphs, based on the assignment restrictions and study the computational complexity of the scheduling problem with respect to structural properties of these graphs, in particular their treeand rankwidth. We identify cases that admit polynomial time approximation schemes or FPT algorithms, generalizing and extending previous results in this area.