Node assignment problem

We consider the following Constraint Satisfaction Problem: Given a set C of constraints in which each constraint has a subset of Variables V that maps to the set of nodes N(T) of a given tree T . Does their exist c: V → N(T) such that for each constraint of C, the variables can take one of the nodes specified in that constraint as its values. This node assignment to the variables is said to be feasible if it satisfies all the constraints. In this paper, we propose an algorithm which will refine the constraints based on the intersection property and will reduce the recursion. Finally the constraints formed do not have intersection with other constraints. We get a feasible assignment by permuting the variables and mapping it to the node set.