We propose a new model for graph editing problems on intersection graphs. In well-studied graph editing problems, adding and deleting vertices and edges are used as graph editing operations. As a graph editing operation on intersection graphs, we propose moving objects corresponding to vertices. In this paper, we focus on interval graphs as an intersection graph. We give a linear-time algorithm to find the total moving distance for transforming an interval graph into a complete graph. The concept of this algorithm can be applied for (i) transforming a unit square graph into a complete graph over $L_1$ distance and (ii) attaining the existence of a $k$-clique on unit interval graphs. In addition, we provide LP-formulations to achieve several properties in the associated graph of unit intervals.

翻译：本文提出了一种针对交集图编辑问题的新模型。在已被广泛研究的图编辑问题中，顶点与边的添加和删除是常见的图编辑操作。针对交集图，我们提出一种以移动对应顶点对象为手段的图编辑操作。本文以区间图作为交集图的具体研究对象，给出了将区间图转换为完全图所需总移动距离的线性时间算法。该算法思想可推广应用于：(i) 在L1距离下将单位正方形图转换为完全图；(ii) 在单位区间图上实现k-团的存在性。此外，我们给出了单位区间关联图中若干性质实现的线性规划形式化描述。