A Practical Approach for Maximizing Satisfiability in Qualitative Spatial and Temporal Constraint Networks

We introduce and study the problem of obtaining a spatial or temporal configuration that maximizes the number of constraints satisfied in a qualitative constraint network (QCN). We call this problem the MAX-QCN problem and prove that it is NP-hard for most of the qualitative calculi. We also propose a complete generic branch and bound algorithm for solving the MAX-QCN problem. This algorithm builds on techniques used in the literature for solving the consistency checking problem and the minimal labeling problem of a given QCN. In particular, we make use of a tractable subclass of relations, a chordal graph provided by a triangulation of the input QCN, and the partial weak composition as a filtering method. The experimentation that we have conducted with QCNs from the Interval Algebra and the Region Connection Calculus shows the interest of our proposed algorithm.