Confluence of the Node-Domination and Edge-Domination Hypergraph Rewrite Rules
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911202504867840 |
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| author | Amarilli, Antoine Monet, Mikaël De Pretto, Rémi |
| author_facet | Amarilli, Antoine Monet, Mikaël De Pretto, Rémi |
| contents | In this note, we study two rewrite rules on hypergraphs, called edge-domination and node-domination, and show that they are confluent. These rules are rather natural and commonly used before computing the minimum hitting sets of a hypergraph. Intuitively, edge-domination allows us to remove hyperedges that are supersets of another hyperedge, and node-domination allows us to remove nodes whose incident hyperedges are a subset of that of another node. We show that these rules are confluent up to isomorphism, i.e., if we apply any sequences of edge-domination and node-domination rules, then the resulting hypergraphs can be made isomorphic via more rule applications. This in particular implies the existence of a unique minimal hypergraph, up to isomorphism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_09286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Confluence of the Node-Domination and Edge-Domination Hypergraph Rewrite Rules Amarilli, Antoine Monet, Mikaël De Pretto, Rémi Data Structures and Algorithms In this note, we study two rewrite rules on hypergraphs, called edge-domination and node-domination, and show that they are confluent. These rules are rather natural and commonly used before computing the minimum hitting sets of a hypergraph. Intuitively, edge-domination allows us to remove hyperedges that are supersets of another hyperedge, and node-domination allows us to remove nodes whose incident hyperedges are a subset of that of another node. We show that these rules are confluent up to isomorphism, i.e., if we apply any sequences of edge-domination and node-domination rules, then the resulting hypergraphs can be made isomorphic via more rule applications. This in particular implies the existence of a unique minimal hypergraph, up to isomorphism. |
| title | Confluence of the Node-Domination and Edge-Domination Hypergraph Rewrite Rules |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2510.09286 |