Breadth first search and inference methods integration to satisfy table constraints

Within the Constraint Programming technology, so-called table constraints such as typical tables, compressed tables, smart tables, segmented tables, etc, are widely used. They can be used to represent any other types of constraints, and algorithms of the table constraint propagation (logical inference on constraints) allow eliminating a lot of "redundant" values from the domains of variables, while having low computational complexity. In the previous studies, the author proposed to divide smart tables into structures of C - and D -types. The generally accepted methodology for solving constraint satisfaction problems is the combined application of constraint propagation methods and backtracking depth-first search methods. In the study, it is proposed to integrate breadth-first search methods and author`s method of table constraint propagation. D-type smart tables are proposed to be represented as a join of several orthogonalized C-type smart tables. The search step is to select a pair of C-type smart tables to be joined and then propagate the restrictions. To determine the order of joining orthogonalized smart tables at each step of the search, a specialized heuristic is used, which reduces the search space, taking into account further calculations. When the restrictions are extended, the acceleration of the computation process is achieved by applying the developed reduction rules for the case of C-type smart tables. The developed hybrid method allows one to find all solutions to the problems of satisfying constraints modeled using one or several D-type smart tables, without decomposing tabular constraints into elementary tuples.