A New Algorithm for the Solution of the Knapsack Problem

A new algorithm for the solution of the knapsack problem is described. The algorithm is based upon successive reductions modulo suitably chosen integers. Thus the original knapsack problem is transformed into a system of modified knapsack problems. Very often a partial solution to the system can be found. The system and the original knapsack can then be reduced to a lower dimensionality and the algorithm repeated. So far we have not been able to characterize the class of knapsack problems for which the algorithm is effective. There are indications, however, that most knapsack problems for which we know that there is one and only one solution may be solved fast by the use of the new algorithm.