Last Conflict Based Reasoning

In this paper, we propose an approach to guide search to sources of conflicts. The principle is the following: the last variable involved in the last conflict is selected in priority, as long as the constraint network can not be made consistent, in order to find the (most recent) culprit variable, following the current partial instantiation from the leaf to the root of the search tree. In other words, the variable ordering heuristic is violated, until a backtrack to the culprit variable occurs and a singleton consistent value is found. Consequently, this way of reasoning can easily be grafted to many search algorithms and represents an original way to avoid thrashing. Experiments over a wide range of benchmarks demonstrate the effectiveness of this approach.