Investigation of one algorithm for solving problems of integer linear programming

A famous algorithm for solving problems of integer linear programming based on the method of regular partitions is investigated. In particular, it is shown that the algorithm is regular with respect to some of such partitions in the case of problems that simplify its application. A subclass of matrices generating such problems is given. A family of problems of special form is constructed for which the algorithm is exponential with respect to the length of the input.