Ng-backmarking - an algorithm for constraint satisfaction

Ng-backmarking with Min-conflict repair, a hybrid algorithm for solving constraint satisfaction problems, is presented in the context of the four main approaches to constraint satisfaction and optimisation: tree-search, domainfiltering, solution repair, and learning while searching. Repair-based techniques are often designed to use local gradients to direct the search for a solution to a constraint satisfaction problem. It has been shown experimentally that such techniques are often well suited to solving large scale problems. One drawback is that they do not guarantee a (optimal) solution if one exists. The motivation behind ng-backmarking is to allow the search to follow local gradients in the search space whilst ensuring a (optimal) solution if one exists. The search space of this combined approach is controlled by the ng-backmarking process, a method of learning constraints during search (at each failure point1) that may be used to avoid the repeated traversing of failed paths in a search tree. In order to control the space of these learned constraints or 'no-goods' we must assess what information can be learned on discovery of a failure by studying the constraints of the CSP (constraint satisfaction problem). To support dynamic constraint satisfaction2 we introduce a strategy for maintaining the set of no-goods.