A multiscale approximation algorithm for the cardinality constrained knapsack problem

Abstract

I develop a multiscale approximation algorithm for the cardinality constrained knapsack problem. The algorithm consists of three steps: a rounding and reduction step where a hierarchical representation of the problem data ranging from coarse to fine is generated, a solution step where a coarse solution is computed, and a refinement step where the accuracy of the solution is improved by refining the problem representation. I demonstrate that the algorithm is fully polynomial with a runtime complexity that improves upon the previous best known fully polynomial approximation scheme. Through an extensive computational study, I show that the running times of the algorithm is less than or equal to that of a commercial integer programming package with little loss in solution accuracy.