Integral knapsack problems: parallel algorithms and their implementations on distributed systems

The parallelization of the dynamic programming algorithm for the integral knapsack problem is approached from several perspectives. Two of them proceed by dividing the set of objects, while a third one proceeds by partitioning the set of capacities. Furthermore, we propose a new sequential algorithm and its parallelization by reducing the integral knapsack problem to a maximum path problem. The theoretical complexity analysis of the algorithms proves that for all the algorithms the product of the number of processors by the parallel time equals the corresponding sequential time. Computational results are presented both for transputer networks using occam and LAN using PVM. Although for many cases the best running times are obtained for the LAN, the speedup and the scalability are better for the transputer network.