Investigation of integer programming problems by means of unimodular transformations and regular partitions

Investigations of questions in integer linear programming are carried out concerned with the joint application of unimodular transformations and the method of regular partitions for changing the structure of problems and increasing the efficiency of algorithms. Main results are obtained for the knapsack problem and some of its generalizations based on an $L$-partition. Families of problems with $L$-coverings of exponential cardinality are presented, and unimodular transformations that improve their structure are constructed. New estimates for the number of iterations are described for $L$-class enumeration algorithms.