Linear algorithm to find minimum subset sum over a threshold

Question

I have a collection of N positive integers, each bounded by a (relatively small) constant C. I want to find a subset of these numbers with the smallest sum greater than (or

Answer 1

Pisinger's algorithm gives you the largest sum less than or equal to the capacity of the knapsack. To solve your problem, use Pisinger to figure out what not to put in the subset. Formally, let the items be w_1, ..., w_n and the minimum be K. Give w_1, ..., w_n and w_1 + ... + w_n - K to Pisinger, then take every item that Pisinger does not.