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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2502.12903 |
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| _version_ | 1866916619427512320 |
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| author | Honorato-Droguett, Nicolás Kurita, Kazuhiro Hanaka, Tesshu Ono, Hirotaka |
| author_facet | Honorato-Droguett, Nicolás Kurita, Kazuhiro Hanaka, Tesshu Ono, Hirotaka |
| contents | We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an $O(n\log n)$-time algorithm that minimises the total moving distance to disperse unit intervals. This algorithm is applied to render a given unit interval graph (i) edgeless, (ii) acyclic and (iii) $k$-clique-free. We next show that GGED becomes strongly NP-hard when rendering a weighted interval graph (i) edgeless, (ii) acyclic and (iii) $k$-clique-free. Lastly, we prove that minimising the maximum moving distance for rendering a unit disk graph edgeless is strongly NP-hard over the $L_1$ and $L_2$ distances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12903 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Complexity of Minimising the Moving Distance for Dispersing Objects Honorato-Droguett, Nicolás Kurita, Kazuhiro Hanaka, Tesshu Ono, Hirotaka Data Structures and Algorithms We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an $O(n\log n)$-time algorithm that minimises the total moving distance to disperse unit intervals. This algorithm is applied to render a given unit interval graph (i) edgeless, (ii) acyclic and (iii) $k$-clique-free. We next show that GGED becomes strongly NP-hard when rendering a weighted interval graph (i) edgeless, (ii) acyclic and (iii) $k$-clique-free. Lastly, we prove that minimising the maximum moving distance for rendering a unit disk graph edgeless is strongly NP-hard over the $L_1$ and $L_2$ distances. |
| title | On the Complexity of Minimising the Moving Distance for Dispersing Objects |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2502.12903 |