Forward Checking with Backmarking

The forward checking routine (FC) of Haralick and Elliott attempts to encourage early failures within the search tree of constraint satisfaction problems, leading to a reduction in nodes visited, which tends to result in reduced search eeort. In contrast, Gaschnig's backmarking routine (BM) attempts to avoid performing redundant consistency checks. These two algorithms are combined to give us FC-BM, an algorithm that attempts to minimise the number of nodes visited, while avoiding redundant consistency checks. This algorithm is further enhanced such that it incorporates connict-directed backjumping (CBJ) to give us FC-BM-CBJ. A series of experiments are then carried out on really hard problems in an attempt to position these new algorithms with respect to the known algorithms.