Modification of the method for developing combinatorial generation algorithms based on the use of multivariate generating functions and approximations

Annotation: This article proposes a modified method for developing combinatorial generation algorithms based on AND/OR trees. The proposed method differs from the original method and its modifications by using the method of obtaining explicit expressions for the coefficients of multivariate generating functions to find the expression for the cardinality function of a given combinatorial set (including combinatorial sets defined by several parameters). Also, the proposed method is distinguished by the use of approximation methods and the binary search to find the selected son of the OR node. This reduces the computational complexity of the unranking algorithms. In order to test the proposed method, a new ranking and unranking algorithms were developed for a combinatorial set of selfavoiding lattice paths. In this case, the use of binary search reduced on average the number of required computational operations and a better computational complexity compared to the original version of the algorithm were obtained.

Keywords: combinatorial generation, multivariate generating functions, approximations, binary search, lattice path, ranking algorithm, unranking algorithm