On Guaranteeing Polynomially Bounded Search Tree Size

Much work has been done on describing tractable classes of constraint networks. Most of the known tractable examples are described by either restricting the structure of the networks, or their language. Indeed, for both structural or language restrictions very strong dichotomy results have been proven and in both cases it is likely that all practical examples have already been discovered. As such it is timely to consider tractability which cannot be described by language or structural restrictions. This is the focus of the work here. In this paper we investigate a novel reason for tractability: having at least one variable ordering for which the number of partial solutions to the first n variables is bounded by a polynomial in n. We show that the presence of sufficient functional constraints can guarantee this property and we investigate the complexity of finding good variable orderings based on different notions of functionality. What is more we identify a completely novel reason for tractability based on so called Turan sets.