Browse Theses

This thesis presents our study of the constraint structure of general constraint satisfaction problems (CSPs). It begins with a review of our previous work on developing two constraint-directed CSP algorithms that solve general CSPs directly without having to transform a CSP to an equivalent binary one. Although this previous work has shown that these two algorithms are more efficient than some related CSP solvers, the complexity of these algorithms are still exponential in the number of variables. This thesis shows that characterizing, analyzing and exploiting the structure of the constraints of the given problem leads to improvement.

To characterize the structure of the constraints of a general CSP, we introduce the ý-graph , which raptures the structure of the constraints more precisely than other related representative graphs, such as the join graph , and thus provides a more effective tool for analyzing and solving CSPs.

Next, we define ý-consistency , which is applicable to both binary and non-binary constraints. Because ý-consistency is stronger than some related forms of consistency, such as pairwise consistency and hyper consistency , it can be used to simplify CSP solving by enforcing a greater degree of consistency.

The thesis goes on to show how the ý-graph and ý-consistency can be used to identify a class of tractable CSPs which properly contains tractable CSPs identified using previously reported methods.

Finally, we present new constraint-directed CSP algorithms which incorporate the ý-graph. We show that if the cyclicity of a CSP's ý-graph is less than a fixed number, these algorithms can solve the CSP in polynomial time.