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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 logarithmic 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.
Lin et al. (Sat,) studied this question.
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