Using auxiliary variables and implied constraints to model non - binaryproblemsBarbara

We perform an extensive theoretical and empirical analysis of the use of auxiliary variables and implied constraints in modelling a class of non-binary constraint satisfaction problems called problems of distance. This class of problems include 1-d, 2-d and circular Golomb rulers. We identify a large number of diierent models, both binary and non-binary, and compare theoretically the level of consistency achieved by generalized arc consistency on them. Our experiments show that the introduction of auxiliary variables and implied constraints can signiicantly reduce the size of the search space. For instance, our nal models reduce the time to nd an optimal 10-mark Golomb ruler 50-fold.