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arXiv · 2501.12848

Approximating Partition in Deterministic Near-Linear Time

Lin Chen·Jiayi Lian·Yuchen Mao·Guochuan Zhang
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Abstract

We propose a deterministic $\widetilde{O}(n + \frac{1}ε)$-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 $\widetilde{O}(n + (\frac{1}ε)^{5/4})$ 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.

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Lin Chen, Jiayi Lian, Yuchen Mao, Guochuan Zhang. 2026-09-23. Approximating Partition in Deterministic Near-Linear Time. https://arxiv.org/abs/2501.12848

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