On the Complexity of Minimising the Moving Distance for Dispersing Objects

• Item type: SIG Technical Reports(1)
• 公開日: 2025-01-07
• タイトル: On the Complexity of Minimising the Moving Distance for Dispersing Objects
• タイトル / 言語: en
• タイトル: On the Complexity of Minimising the Moving Distance for Dispersing Objects
• 言語: eng
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_18gh
• 資源タイプ: technical report
• 著者所属: Department of Mathematical Informatics, Graduate School of Informatics, Nagoya University
• 著者所属: Department of Mathematical Informatics, Graduate School of Informatics, Nagoya University
• 著者所属: Department of Informatics, Faculty of Information Science and Electrical Engineering, Kyushu University
• 著者所属: Department of Mathematical Informatics, Graduate School of Informatics, Nagoya University
• 著者所属(英): en
• 著者所属(英): Department of Mathematical Informatics, Graduate School of Informatics, Nagoya University
• 著者所属(英): en
• 著者所属(英): Department of Mathematical Informatics, Graduate School of Informatics, Nagoya University
• 著者所属(英): en
• 著者所属(英): Department of Informatics, Faculty of Information Science and Electrical Engineering, Kyushu University
• 著者所属(英): en
• 著者所属(英): Department of Mathematical Informatics, Graduate School of Informatics, Nagoya University
• 著者名: Nicolás, Honorato Droguett; Kazuhiro, Kurita; Tesshu, Hanaka; Hirotaka, Ono
• 著者名(英): Nicolás, Honorato Droguett; Kazuhiro, Kurita; Tesshu, Hanaka; Hirotaka, Ono
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Graph Edit Distance (GED) is one of the distance measures that excels in inexact graph matching, typically computed through additions and deletions of vertices and edges. We introduce Geometric Graph Edit Distance (GGED), a novel GED-based model for computing the edit distance of intersection graphs that uses moving objects as an edit operation. This paper addresses the tractability of GGED problems for graph properties that require objects to be dispersed from each other. We first show a O(nm)-time algorithm that minimises the total moving distance to disperse intervals. This algorithm is applied to transform a given unit interval graph into an (i) edgeless, (ii) acyclic, (iii) k-clique-free, (iv) bipartite and (v) planar graphs. We next prove that minimising the maximum moving distance for transforming a unit disk graph into an edgeless graph is NP-hard over L1 and L2 distances. Finally, we provide LP formulations of the minimax GGED to achieve several graph properties on unit interval graphs.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Graph Edit Distance (GED) is one of the distance measures that excels in inexact graph matching, typically computed through additions and deletions of vertices and edges. We introduce Geometric Graph Edit Distance (GGED), a novel GED-based model for computing the edit distance of intersection graphs that uses moving objects as an edit operation. This paper addresses the tractability of GGED problems for graph properties that require objects to be dispersed from each other. We first show a O(nm)-time algorithm that minimises the total moving distance to disperse intervals. This algorithm is applied to transform a given unit interval graph into an (i) edgeless, (ii) acyclic, (iii) k-clique-free, (iv) bipartite and (v) planar graphs. We next prove that minimising the maximum moving distance for transforming a unit disk graph into an edgeless graph is NP-hard over L1 and L2 distances. Finally, we provide LP formulations of the minimax GGED to achieve several graph properties on unit interval graphs.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AN1009593X
• 書誌情報: 研究報告アルゴリズム（AL）; 巻 2025-AL-201, 号 13, p. 1-4, 発行日 2025-01-07
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 2188-8566
• Notice: SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc.
• 出版者 / 言語: ja
• 出版者: 情報処理学会