New pseudopolynomial complexity bounds for the bounded and other integer Knapsack related problems

We consider the bounded integer knapsack problem (BKP) , subject to: , and x_j{0,1,…,m_j},j=1,…,n. We use proximity results between the integer and the continuous versions to obtain an O(n³W²) algorithm for BKP, where W=max_j=1,…,nw_j. The respective complexity of the unbounded case with m_j=∞, for j=1,…,n, is O(n²W²). We use these results to obtain an improved strongly polynomial algorithm for the multicover problem with cyclical 1’s and uniform right-hand side.