An Improved Pseudopolynomial Time Algorithm for Subset Sum
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910170737541120 |
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| author | Chen, Lin Lian, Jiayi Mao, Yuchen Zhang, Guochuan |
| author_facet | Chen, Lin Lian, Jiayi Mao, Yuchen Zhang, Guochuan |
| contents | We investigate pseudo-polynomial time algorithms for Subset Sum. Given a multi-set $X$ of $n$ positive integers and a target $t$, Subset Sum asks whether some subset of $X$ sums to $t$. Bringmann proposes an $\tilde{O}(n + t)$-time algorithm [Bringmann SODA'17], and an open question has naturally arisen: can Subset Sum be solved in $O(n + w)$ time? Here $w$ is the maximum integer in $X$. We make a progress towards resolving the open question by proposing an $\tilde{O}(n + \sqrt{wt})$-time algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Improved Pseudopolynomial Time Algorithm for Subset Sum Chen, Lin Lian, Jiayi Mao, Yuchen Zhang, Guochuan Data Structures and Algorithms We investigate pseudo-polynomial time algorithms for Subset Sum. Given a multi-set $X$ of $n$ positive integers and a target $t$, Subset Sum asks whether some subset of $X$ sums to $t$. Bringmann proposes an $\tilde{O}(n + t)$-time algorithm [Bringmann SODA'17], and an open question has naturally arisen: can Subset Sum be solved in $O(n + w)$ time? Here $w$ is the maximum integer in $X$. We make a progress towards resolving the open question by proposing an $\tilde{O}(n + \sqrt{wt})$-time algorithm. |
| title | An Improved Pseudopolynomial Time Algorithm for Subset Sum |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2402.14493 |