Upper and lower bounds for the complexity of the branch and bound method for the knapsack problem

This paper is devoted to questions concerning the complexity of solution of the problem on one-dimensional Boolean knapsack by the branch and bound method. For this complexity we obtain two upper bounds. We separate the special case of the knapsack problem where the complexity is polynomially hounded by the dimension of the problem. We also obtain an upper and lower bounds for the complexity of solution by the branch and hound method of the subset sum problem which is a special case of the knapsack problem. This research was supported by the Russian Foundation for Basic Research, grants 05-01-00495-a and 06-07-89079-a.