An approximation algorithm for zero forcing
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913234318000128 |
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| author | Cameron, Ben Janssen, Jeannette Matthew, Rogers Zhang, Zhiyuan |
| author_facet | Cameron, Ben Janssen, Jeannette Matthew, Rogers Zhang, Zhiyuan |
| contents | We give an algorithm that finds a zero forcing set which approximates the optimal size by a factor of $\text{pw}(G)+1$, where $\text{pw}(G)$ is the pathwidth of $G$. Starting from a path decomposition, the algorithm runs in $O(nm)$ time, where $n$ and $m$ are the order and size of the graph, respectively. As a corollary, we obtain a new upper bound on the zero forcing number in terms of the fort number and the pathwidth. The algorithm is based on a correspondence between zero forcing sets and forcing arc sets. This correspondence leads to a new bound on the zero forcing number in terms of vertex cuts, and to new, short proofs for known bounds on the zero forcing number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An approximation algorithm for zero forcing Cameron, Ben Janssen, Jeannette Matthew, Rogers Zhang, Zhiyuan Combinatorics We give an algorithm that finds a zero forcing set which approximates the optimal size by a factor of $\text{pw}(G)+1$, where $\text{pw}(G)$ is the pathwidth of $G$. Starting from a path decomposition, the algorithm runs in $O(nm)$ time, where $n$ and $m$ are the order and size of the graph, respectively. As a corollary, we obtain a new upper bound on the zero forcing number in terms of the fort number and the pathwidth. The algorithm is based on a correspondence between zero forcing sets and forcing arc sets. This correspondence leads to a new bound on the zero forcing number in terms of vertex cuts, and to new, short proofs for known bounds on the zero forcing number. |
| title | An approximation algorithm for zero forcing |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.08866 |