The Brélaz Heuristic and Optimal Static Orderings

The order in which the variables are assigned can have an enormous impact on the time taken by a backtracking search algorithm to solve a constraint satisfaction problem (CSP). The Br'elaz heuristic is a dynamic variable ordering heuristic which has been shown to give good results for some classes of binary CSPs when the constraint graph is not complete. Its advantage over the simpler smallest-domain heuristic is that it uses information about the constraint graph. This paper uses theoretical work by Nudel to assess the performance of the Br'elaz heuristic. Nudel's work gives the expected number of nodes at each level of the search tree when using the forward checking algorithm to find all solutions to a CSP, given a specified order of the variables. From this, optimal static orderings are found for a sample of small binary CSPs. The optimal orderings are used to learn rules for a static ordering heuristic, which are converted into modifications to the Br'elaz heuristic. ..