When functional and bijective constraints make a CSP polynomial

摘要

Many works have been carried out to improve search efficiency in CSPs, but few of them treated the semantics of the constraints. In this paper, we expose some properties of two classes of constraints, functional and bijective constraints: we first present conditions under which arc and path consistencies are sufficient to guarantee the existence of a bactrack free solution; we then exhibit classes of polynomial problems, and finally we propose a new method of decomposition for problems containing functional or bijective constraints. An interesting point in this method is that the resolution complexity is known prior to the search.