Efficiently Explaining CSPs with Unsatisfiable Subset Optimization

Abstract

We build on a recently proposed method for stepwise explaining the solutions to Constraint Satisfaction Problems (CSPs) in a human understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified by a cost function. Explanation generation algorithms rely on extracting Minimal Unsatisfiable Subsets (MUSs) of a derived unsatisfiable formula, exploiting a one-to-one correspondence between so-called non-redundant explanations and MUSs. However, MUS extraction algorithms do not guarantee subset minimality or optimality with respect to a given cost function. Therefore, we build on these formal foundations and address the main points of improvement, namely how to generate explanations efficiently that are provably optimal (with respect to the given cost metric). To this end, we developed (1) a hitting set-based algorithm for finding the optimal constrained unsatisfiable subsets; (2) a method for reusing relevant information across multiple algorithm calls; and (3) methods for exploiting domain-specific information to speed up the generation of explanation sequences. We have experimentally validated our algorithms on a large number of CSP problems. We found that our algorithms outperform the MUS approach in terms of explanation quality and computational time (on average up to 56 % faster than a standard MUS approach).