OASIcs.SOSA.2019.17.pdf
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A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum
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2nd Symposium on Simplicity in Algorithms (SOSA 2019)
Series: Open Access Series in Informatics (OASIcs) - License:
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- Publication Date: 2019-01-08
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Ce Jin and Hongxun Wu. A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 17:1-17:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/OASIcs.SOSA.2019.17
https://doi.org/10.4230/OASIcs.SOSA.2019.17
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 O~(sqrt{n}t) time, where O~ hides poly-logarithm factors. Bringmann [SODA'17] later gave a randomized O~(n + t) time algorithm using two-stage color-coding. The 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 O~(n + t) time. Our new algorithm actually solves its counting version modulo prime p>t, by manipulating generating functions using FFT.
Keywords
- subset sum
- formal power series
- FFT
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References
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