On the equal-subset-sum problem
Information Processing Letters
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Approximation algorithms
Efficient approximation algorithms for the subset-sums equality problem
Journal of Computer and System Sciences
On the complexity of variations of equal sum subsets
Nordic Journal of Computing
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In the subset-sums ratio problem, we want to find two sets of numbers such that the ratio between the larger and smaller sets (in terms of the summed values) is as small as possible. We show a new Fully Polynomial-Time Approximation Scheme (FPTAS) for this problem which simplifies the algorithm proposed by [C. Bazgan, M. Santha, Z. Tuza, Efficient approximation algorithms for the SUBSET-SUMS EQUALITY problem, J. Comput. System Sci. 64 (2) (2002) 160-170, announced in ICALP 1998]. The key insight of the new algorithm is to solve the problem with an additional constraint that the output sets must contain some certain numbers. While the new problem is harder (in the sense that the original problem can be reduced to this problem), it still admits an FPTAS, which is surprisingly simpler than the FPTAS of the original problem.