Dynamic Variable Ordering in CSPs

We investigate the dynamic variable ordering (DVO) technique commonly used in conjunction with tree-search algorithms for solving constraint satisfaction problems. We first provide an implementation methodology for adding DVO to an arbitrary tree-search algorithm. Our methodology is applicable to a wide range of algorithms including those that maintain complicated information about the search history, like backmarking. We then investigate the popular reordering heuristic of next instantiating the variable with the minimum remaining values (MRV). We prove some interesting theorems about the MRV heuristic which demonstrate that if one wants to use the MRV heuristic one may as well use it with forward checking. Finally, we investigate the empirical performance of 12 different algorithms with and without DVO. Our experiments and theoretical results demonstrate that forward checking equipped with dynamic variable ordering is a very good algorithm for solving CSPs.