On total functions, existence theorems and computational complexity
Theoretical Computer Science
On the equal-subset-sum problem
Information Processing Letters
On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
An Efficient Approximation Scheme for the Subset-Sum Problem
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
On the complexity of variations of equal sum subsets
Nordic Journal of Computing
Simple FPTAS for the subset-sums ratio problem
Information Processing Letters
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We investigate the problem of finding two nonempty disjoint subsets of a set of n positive integers, with the objective that the sums of the numbers in the two subsets be as close as possible. In two versions of this problem, the quality of a solution is measured by the ratio and the difference of the two partial sums, respectively. Answering a problem of G. J. Woeginger and Z. Yu (1992, Inform. Process. Lett. 42, 299-302) in the affirmative, we give a fully polynomial-time approximation scheme for the case where the value to be optimized is the ratio between the sums of the numbers in the two sets. On the other hand, we show that in the case where the value of a solution is the positive difference between the two partial sums, the problem is not 2nk -approximable in polynomial time unless P = NP, for any constant k. In the positive direction, we give a polynomial time algorithm that finds two subsets for which the difference of the two sums does not exceed K/nΩ(log n), where K is the greatest number in the instance.