An algorithm and efficient data structures for the binary knapsack problem

A branch-and-bound algorithm for the binary knapsack problem is presented which uses a combined stack and deque for storing the tree and the corresponding LP-relaxation. A reduction scheme is used to reduce the problem size. The algorithm was implemented in FORTRAN. Computational experience is based on 600 randomly generated test problems with up to 9000 zero-one variables. The average solution times (excluding an initial sorting step) increase linearly with problem size and compare favorably with other codes designed to solve binary knapsack problems.