Using pivot consistency to decompose and solve functional CSPs
Résumé
Many studies have been carried out in order to increase the search efficiency of constraint satisfaction problems; among them, some make use of {\em structural} properties of the constraint network; others take into account {\em semantic} properties of the constraints, generally assuming that {\em all} the constraints possess the given property. In this paper, we propose a new decomposition method benefiting from both semantic properties of {\em functional} constraints (not {\em bijective} constraints) and structural properties of the network; furthermore, not all the constraints need to be functional. We show that under some conditions, the existence of solutions can be guaranteed. We first characterize a particular subset of the variables, which we name a {\em root set}. We then introduce {\em pivot consistency}, a new local consistency which is a we ak form of path consistency and can be achieved in $O(n^2d^2)$ complexity (instead of $O(n^3d^3)$ for path consistency), and we present associated properti es; in particular, we show that any consistent instantiation of the root set can be linearly extended to a solution, which leads to the presentation of the aforementioned new method for solving by decomposing functional {\sc csp}s.