An algorithm with a delay of $\mathcal{O}(kΔ)$ for enumerating connected induced subgraphs of size $k$
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911043137044480 |
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| author | Xiao, Chenglong Mao, Chengyong Wang, Shanshan |
| author_facet | Xiao, Chenglong Mao, Chengyong Wang, Shanshan |
| contents | The problem of enumerating connected subgraphs of a given size in a graph has been extensively studied in recent years. In this paper, we propose an algorithm with a delay of $O(kΔ)$ for enumerating all connected induced subgraphs of size $k$ in an undirected graph $G=(V, E)$, where $k$ and $Δ$ are respectively the size of subgraphs and the maximum degree of $G$. The algorithm requires a preprocessing step of $O(|V| + |E|)$ time to compute a depth-first search traversal order. The proposed algorithm improves upon the current best delay bound $O(k^2Δ)$ for the connected induced subgraph enumeration problem in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An algorithm with a delay of $\mathcal{O}(kΔ)$ for enumerating connected induced subgraphs of size $k$ Xiao, Chenglong Mao, Chengyong Wang, Shanshan Data Structures and Algorithms Discrete Mathematics The problem of enumerating connected subgraphs of a given size in a graph has been extensively studied in recent years. In this paper, we propose an algorithm with a delay of $O(kΔ)$ for enumerating all connected induced subgraphs of size $k$ in an undirected graph $G=(V, E)$, where $k$ and $Δ$ are respectively the size of subgraphs and the maximum degree of $G$. The algorithm requires a preprocessing step of $O(|V| + |E|)$ time to compute a depth-first search traversal order. The proposed algorithm improves upon the current best delay bound $O(k^2Δ)$ for the connected induced subgraph enumeration problem in the literature. |
| title | An algorithm with a delay of $\mathcal{O}(kΔ)$ for enumerating connected induced subgraphs of size $k$ |
| topic | Data Structures and Algorithms Discrete Mathematics |
| url | https://arxiv.org/abs/2404.12559 |