Accelerating Greenberg's metho̧d for the computation of knapsack functions

Jonathan S Yormark
1975 Journal of Mathematical Analysis and Applications  
Submitted by Richard Bellman Greenberg [4] described an interesting procedure based on dynamic programming for generating the knapsack function @p(s) = max{cx: ax < s, x > 0, integer) for all arguments s < b, where c, a, and x are vectors with nonnegative integer components and b is a positive integer. The principle search effort can be associated with finding the minimum of a string D of K elements. It is shown here that a rank ordering of the components of a yields sequences D such that a
more » ... ch for the minimum in D over the first m elements is sufficient. In general, m is smaller than K and the calculation of @ is accelerated. Extensions of the basic procedure to the case where the components of x have upper-bounds is also described.
doi:10.1016/0022-247x(75)90202-4 fatcat:33rfnukl2rhppkldvn7tush5om