1. An Improved Pseudopolynomial Time Algorithm for Subset Sum
- Author
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Chen, Lin, Lian, Jiayi, Mao, Yuchen, and Zhang, Guochuan
- Subjects
Computer Science - Data Structures and Algorithms - Abstract
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., Comment: In first version, we falsely claimed that our algorithm is also able to reconstruct a subset that sums to t. In the latest version, we removed this false claim and explained why we cannot do reconstruction
- Published
- 2024