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 $L_\infty$ 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：我们提出了一种新的交图编辑问题模型。在传统的图编辑问题中，增删顶点和边是常用的图编辑操作。本文针对交图提出了一种新的图编辑操作——移动顶点对应的对象。具体以区间图（一种交图）为例，我们给出了一个线性时间算法，用于计算将区间图转化为完全图所需的移动总距离。该算法思想可应用于：(i) 在$L_\infty$距离下将单位正方形图转化为完全图；(ii) 在单位区间图中实现$k$-团的存在性。此外，我们还给出了线性规划形式化描述，以实现单位区间关联图的若干性质。