@techreport{oai:ipsj.ixsq.nii.ac.jp:00241901,
 author = {Nicolás, Honorato Droguett and Kazuhiro, Kurita and Tesshu, Hanaka and Hirotaka, Ono and Nicolás, Honorato Droguett and Kazuhiro, Kurita and Tesshu, Hanaka and Hirotaka, Ono},
 issue = {13},
 month = {Jan},
 note = {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., 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.},
 title = {On the Complexity of Minimising the Moving Distance for Dispersing Objects},
 year = {2025}
}