Complexity in Constraint Satisfaction and Automated Configuration

The Partner Units Problem (Pup) is a new benchmark configuration problem. This problem involves the configuration of a network of sensors and controllers, and has drawn significant attention due to the amount of industrial applications it finds. In this dissertation, we further explored previous work done on a tractable class of the problem, exploiting the notion of a path decomposition, representing and re-evaluating the encodings for the general version of the problem. During this endeavor, through constraint satisfaction methods, we presented new implied constraints and search conditions, which resulted in a number of results that give us new insight into the problem. Next, we extensively presented all the classes of the problem and analyzed their complexity, a problem that had been left open. Interestingly enough, the discrepancy between the classes of the problem was significant in terms of their structural properties. The complexity analysis showed that all the non trivial classes seem to belong in NP-Complete (some were proven and others were conjectured), and even the most trivial classes of the problem were proven to be solvable only in PTime. Finally, we presented a logical approach to the Pup; we used two algorithmic meta-theorems to approach and tackle the complexity of our unsolved classes. In doing so we discovered a new configuration problem, the Partner Units Embedding Problem, which we analyzed and proved to be fixed-point linear in respect to the treewidth of the input graphs.