On Robustness in Qualitative Constraint Networks

We introduce and study a notion of robustness in Qualitative Constraint Networks (QCNs), which are typically used to represent and reason about abstract spatial and temporal information. In particular, given a QCN, we are interested in obtaining a robust qualitative solution, or, a robust scenario of it, which is a satisfiable scenario that has a higher perturbation tolerance than any other, or, in other words, a satisfiable scenario that has more chances than any other to remain valid after it is altered. This challenging problem requires to consider the entire set of satisfiable scenarios of a QCN, whose size is usually exponential in the number of constraints of that QCN; however, we present a first algorithm that is able to compute a robust scenario of a QCN using linear space in the number of constraints. Preliminary results with a dataset from the job-shop scheduling domain, and a standard one, show the interest of our approach and highlight the fact that not all solutions are created equal.