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arXiv · 1807.11597

A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum

Ce Jin·Hongxun Wu
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Abstract

Given a multiset $S$ of $n$ positive integers and a target integer $t$, the Subset Sum problem asks to determine whether there exists a subset of $S$ that sums up to $t$. The current best deterministic algorithm, by Koiliaris and Xu [SODA'17], runs in $\tilde O(\sqrt{n}t)$ time, where $\tilde O$ hides poly-logarithm factors. Bringmann [SODA'17] later gave a randomized $\tilde O(n + t)$ time algorithm using two-stage color-coding. The $\tilde O(n+t)$ running time is believed to be near-optimal. In this paper, we present a simple and elegant randomized algorithm for Subset Sum in $\tilde O(n + t)$ time. Our new algorithm actually solves its counting version modulo prime $p>t$, by manipulating generating functions using FFT.

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Ce Jin, Hongxun Wu. 2018-11-26. A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum. https://doi.org/10.4230/oasics.sosa.2019.17

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