A Deterministic Fully Polynomial Time Approximation Scheme For Counting Integer Knapsack Solutions Made Easy

Given $n$ elements with nonnegative integer weights $w=(w_1,\ldots,w_n)$, an integer capacity $C$ and positive integer ranges $u=(u_1,\ldots,u_n)$, we consider the counting version of the classic integer knapsack problem: find the number of distinct multisets whose weights add up to at most $C$. We give a deterministic algorithm that estimates the number of solutions to within … Read more