An Efficient Approximation Scheme for the Subset-Sum Problem
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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 ɛ in time O(minn/g3 n + 1/g32 log(1/ɛ)) and space O(n + 1/ɛ). The scheme has better time and space complexity than other known approximation schemes.
[1] Oscar H. Ibarra,et al. Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems , 1975, JACM.
[2] Eugene L. Lawler,et al. Fast approximation algorithms for knapsack problems , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).
[3] Eugene Levner,et al. Fast approximation algorithms for knapsack type problems , 1980 .