Approximating subset sum ratio via partition computations

We present a new FPTAS for the Subset Sum Ratio problem, which, given a set of integers, asks for two disjoint subsets such that the ratio of their sums is as close to 1 as possible. Our scheme makes use of exact and approximate algorithms for Partition , and clearly showcases the close relationship between the two algorithmic problems. Depending on the relationship between the size of the input set n and the error margin ε , we improve upon the best currently known algorithm of Melissinos and Pagourtzis [COCOON 2018] of complexity 𝒪 (n^4 / ε ) . In particular, the exponent of n in our proposed scheme may decrease down to 2, depending on the Partition algorithm used.