Approximation Schemes for 0-1 Knapsack

We revisit the standard 0-1 knapsack problem. The latest polynomial-time approximation scheme by Rhee (2015) with approximation factor 1+eps has running time near O(n+(1/eps)^{5/2}) (ignoring polylogarithmic factors), and is randomized. We present a simpler algorithm which achieves the same result and is deterministic. With more effort, our ideas can actually lead to an improved time bound near O(n + (1/eps)^{12/5}), and still further improvements for small n