An efficient approximation scheme for the subset-sum problem

Abstract

Given a set of n positive integers and a knapsack of capacity c, the Subset-Sum Problem is to find a subset the sum of which is closest to c without exceeding the value c. In this paper we present a fully polynomial approximation scheme which solves the subset-sum problem with accuracy e in time O(min{n/ɛ, n + 1/ɛ2 log(1/ɛ)}) and space O(n + 1/ɛ). The scheme has better time and space complexity than other known approximation schemes.