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On the Complexity of Minimising the Moving Distance for Dispersing Objects

Authors Nicolás Honorato-Droguett , Kazuhiro Kurita , Tesshu Hanaka , Hirotaka Ono

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  • Theory of computation → Mathematical optimization
Keywords
  • Intersection graphs
  • Optimisation
  • Graph modification

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Abstract

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 L₁ and L₂ distances.

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Nicolás Honorato-Droguett, Kazuhiro Kurita, Tesshu Hanaka, and Hirotaka Ono. On the Complexity of Minimising the Moving Distance for Dispersing Objects. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.36

Author Details

Nicolás Honorato-Droguett
  • Nagoya University, Japan
Kazuhiro Kurita
  • Nagoya University, Japan
Tesshu Hanaka
  • Kyushu University, Fukuoka, Japan
Hirotaka Ono
  • Nagoya University, Japan

Funding

  • Kurita, Kazuhiro: This work is partially supported by JSPS KAKENHI Grant Numbers JP21K17812, JP22H03549, and JST ACT-X Grant Number JPMJAX2105.
  • Hanaka, Tesshu: This work is partially supported by JSPS KAKENHI Grant Numbers JP21K17707, JP23H04388, JST CRONOS Grant Number JPMJCS24K2.
  • Ono, Hirotaka: This work is partially supported by JSPS KAKENHI Grant Numbers JP20H05967, JP21K19765, JP22H00513, JST CRONOS Grant Number JPMJCS24K2.

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