Estimation of the number of iterations in integer programming algorithms using the regular partitions method

We review the results of studying integer linear programming algorithms which exploit properties of problem relaxation sets. The main attention is paid to the estimation of the number of iterations of these algorithms by means of the regular partitions method and other approaches. We present such estimates for some cutting plane, branch and bound (Land and Doig scheme), and L -class enumeration algorithms and consider questions of their stability. We establish the upper bounds for the average number of iterations of the mentioned algorithms as applied to the knapsack problem and the set packing one.