Approximating Partition in Near-Linear Time

We propose an O(n + 1/)-time FPTAS (Fully Polynomial-Time Approximation Scheme) for the classical Partition problem. This is the best possible (up to a polylogarithmic factor) assuming SETH (Strong Exponential Time Hypothesis) Abboud, Bringmann, Hermelin, and Shabtay'22. Prior to our work, the best known FPTAS for Partition runs in O(n + 1/5/4) time Deng, Jin and Mao'23, Wu and Chen'22. Our result is obtained by solving a more general problem of weakly approximating Subset Sum.