Approximation algorithms for knapsack problems with cardinality constraints
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding. As an application of these techniques, we present a faster polynomial time approximation scheme requiring only linear storage, that computes an approximate solution of any xed accuracy in linear time. This linear complexity bound gives a substantial improvement of the best previously known polynomial bound 2].