Analysis of integer programming algorithms with $L$-partition and unimodular transformations

We study algorithms for solving integer linear programming problems, in particular, set packing and knapsack problems. We pay special attention to algorithms of lexicographic enumeration of $L$-classes and their combinations with other approaches. We study the problems of using unimodular transformations in order to improve the structure of the problems and speed up the algorithms. We construct estimates on the number of iterations for the algorithms that take into account the specific structure of the problems in question. We also show experimental results.