Blazing a Trail via Matrix Multiplications: A Faster Algorithm for Non-shortest Induced Paths
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866914960849764352 |
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| author | Chiu, Yung-Chung Lu, Hsueh-I |
| author_facet | Chiu, Yung-Chung Lu, Hsueh-I |
| contents | For vertices $u$ and $v$ of an $n$-vertex graph $G$, a $uv$-trail of $G$ is an induced $uv$-path of $G$ that is not a shortest $uv$-path of $G$. Berger, Seymour, and Spirkl [Discrete Mathematics 2021] gave the previously only known polynomial-time algorithm, running in $O(n^{18})$ time, to either output a $uv$-trail of $G$ or ensure that $G$ admits no $uv$-trail. We reduce the complexity to the time required to perform a poly-logarithmic number of multiplications of $n^2\times n^2$ Boolean matrices, leading to a largely improved $O(n^{4.75})$-time algorithm. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2109_15268 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Blazing a Trail via Matrix Multiplications: A Faster Algorithm for Non-shortest Induced Paths Chiu, Yung-Chung Lu, Hsueh-I Data Structures and Algorithms Discrete Mathematics 05C38, 05C10, 05C85, 68P05 For vertices $u$ and $v$ of an $n$-vertex graph $G$, a $uv$-trail of $G$ is an induced $uv$-path of $G$ that is not a shortest $uv$-path of $G$. Berger, Seymour, and Spirkl [Discrete Mathematics 2021] gave the previously only known polynomial-time algorithm, running in $O(n^{18})$ time, to either output a $uv$-trail of $G$ or ensure that $G$ admits no $uv$-trail. We reduce the complexity to the time required to perform a poly-logarithmic number of multiplications of $n^2\times n^2$ Boolean matrices, leading to a largely improved $O(n^{4.75})$-time algorithm. |
| title | Blazing a Trail via Matrix Multiplications: A Faster Algorithm for Non-shortest Induced Paths |
| topic | Data Structures and Algorithms Discrete Mathematics 05C38, 05C10, 05C85, 68P05 |
| url | https://arxiv.org/abs/2109.15268 |