| Abstract: | Constraint satisfaction problems are ubiquitous in artificial intelligence and many algorithms have been developed for their solution. This paper provides a unified survey of some of these, in terms of three classes: (i) tree search, (ii) arc consistency (AC), and (iii) hybrid tree search/arc consistency algorithms. It is shown that several important algorithms, when slightly rearranged, are of the latter hybrid form, but with arc consistency components that do not necessarily achieve full arc consistency at the tree nodes. Accordingly, we define several new partial AC procedures, AC1/5, AC1/4, AC1/3, and AC½, analogous to the well-known full AC algorithms which Mackworth has called AC1, AC2, and AC3. The fractional suffixes on our AC algorithms are roughly proportional to the degree of partial arc consistency they achieve. Unlike traditional versions, our AC algorithms (full and partial) are presented in a parameterized form to allow them to be embedded efficiently at the nodes of a tree search process. Algorithm complexities are compared empirically, using the n-queens problem and a new version called confused n-queens. Gaschnig's Backmarking (a tree search algorithm) and Haralick's Forward Checking (a hybrid algorithm) are found to be the most efficient. For the hybrid algorithms, we find that it pays to do little arc consistency processing at the nodes, incurring more nodes, but sufficiently reducing the work per node so as to obtain less work over the whole tree. The unified view taken here suggests several new algorithms. Preliminary results show one of these to be the best algorithm so far. |
