A graph-theoretic approach for recognizing the user interpretation without conflicts

In order to express user interpretation (a set of user-specified GD-constraints (Z. Tari et al., 1997)), in terms of a directed graph, the definition of directed graph in graph theory is extended according to the characters of the user interpretation and the requirement of the problem; the node in this directed graph may be either an ordinary node or a directed graph. The directed graph (having been extended) expressing the user interpretation, is said to be a GD-constraint graph. Based on this, the features of the GD-constraint graph corresponding to the user interpretation without conflicts are extracted. Finally, the sufficient and necessary condition under which the user interpretation doesn't contain conflicts is given, and a polynomial time recognition algorithm whose time complexity is O(m*n), is proposed on the basis of the sufficient and necessary condition. Next, the correctness of the algorithm is proved and the time complexity of the algorithm is analyzed.