Efficient Relaxations of Over-constrained CSPs

Constraint Programming is becoming the preferred solving technology in a variety of application domains. It is not unusual that a CSP modeling some real-life problem is found to be unfeasible or over-constrained. In this scenario, users may be interested in identifying the causes responsible for inconsistency, or in getting some advice so that they can reformulate their problem to render it feasible. This paper is concerned with the latter issue, which plays a very important role in the analysis of over-constrained problems. Concretely, we study the problem of computing a minimal exclusion set of constraints (MESC) from unfeasible CSPs. A MESC is a set-wise minimal set of constraints whose removal makes the original problem feasible. We provide an overview of existing techniques for MESC extraction and consider additional alternatives and optimizations. Our main contribution is the adaptation of one of the best-performing algorithms for SAT to work in CSP. We also integrate a technique that improves its efficiency. The results from an experimental study indicate considerable improvements over the state-of-the-art.