English

A Note on Deterministic FPTAS for Partition

Data Structures and Algorithms 2025-01-23 v1

Abstract

We consider the Partition problem and propose a deterministic FPTAS (Fully Polynomial-Time Approximation Scheme) that runs in O~(n+1/ε)\widetilde{O}(n + 1/\varepsilon)-time. This is the best possible (up to a polylogarithmic factor) assuming the Strong Exponential Time Hypothesis~[Abboud, Bringmann, Hermelin, and Shabtay'22]. Prior to our work, only a randomized algorithm can achieve a running time of O~(n+1/ε)\widetilde{O}(n + 1/\varepsilon)~[Chen, Lian, Mao and Zhang '24], while the best deterministic algorithm runs in O~(n+1/ε5/4)\widetilde{O}(n+1/\varepsilon^{5/4}) time~[Deng, Jin and Mao '23] and [Wu and Chen '22].

Keywords

Cite

@article{arxiv.2501.12848,
  title  = {A Note on Deterministic FPTAS for Partition},
  author = {Lin Chen and Jiayi Lian and Yuchen Mao and Guochuan Zhang},
  journal= {arXiv preprint arXiv:2501.12848},
  year   = {2025}
}
R2 v1 2026-06-28T21:13:32.368Z