A faster FPTAS for the subset-sums ratio problem

Abstract

The Subset-Sums Ratio problem (SSR) is an optimization problem in which, given a set of integers, the goal is to find two subsets such that the ratio of their sums is as close to 1 as possible. In this paper we develop a new FPTAS for the SSR problem which builds on techniques proposed by Nanongkai (Inf Proc Lett 113, 2013). One of the key improvements of our scheme is the use of a dynamic programming table in which one dimension represents the difference of the sums of the two subsets. This idea, together with a careful choice of a scaling parameter, yields an FPTAS that is several orders of magnitude faster than the best currently known scheme of Bazgan et al. (J Comput Syst Sci 64(2), 2002).