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Auteurs principaux: Honorato-Droguett, Nicolás, Kurita, Kazuhiro, Hanaka, Tesshu, Ono, Hirotaka
Format: Preprint
Publié: 2025
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Accès en ligne:https://arxiv.org/abs/2502.12903
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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