We study the algorithmic problem of computing drawings of graphs in which (i) each vertex is a disk with fixed radius ρ, $(ii)$ each edge is a straight-line segment connecting the centers of the two disks representing its end-vertices, $(iii)$ no two disks intersect, and $(iv)$ the distance between an edge segment and the center of a non-incident disk, called edge-vertex resolution, is at least ρ. We call such drawings disk-link drawings.

In this paper we focus on the case of constant edge-vertex resolution, namely $\rho =\frac{1}{2}$ (i.e., disks of unit diameter). We prove that star graphs, which trivially admit straight-line drawings in linear area, require quadratic area in any such disk-link drawing. On the positive side, we present constructive techniques that yield improved upper bounds for the area requirements of disk-link drawings for several (planar and nonplanar) graph classes, including bounded bandwidth, complete, and planar graphs. In particular, the presented bounds for complete and planar graphs are asymptotically tight.

我们研究计算图形绘图的算法问题，其中（i）每个顶点是半径为ρ的圆盘，$（\mathrm{一世}\mathrm{一世}）$ 每个边缘都是一条直线段，连接代表其末端顶点的两个圆盘的中心， $（\mathrm{一世}\mathrm{一世}\mathrm{一世}）$ 没有两个磁盘相交，并且 $（\mathrm{一世}v）$边缘段与非入射磁盘中心之间的距离，称为边缘顶点分辨率，至少为ρ。我们称此类图纸为磁盘链接图纸。

在本文中，我们关注恒定边顶点分辨率的情况，即 $\rho =\frac{\mathrm{1个}}{\mathrm{2个}}$（即单位直径的圆盘）。我们证明了星形图（在平凡的线性区域中允许直线图形接受）在任何此类磁盘链接图形中都需要平方区域。从积极的方面来看，我们提出了一些建设性的技术，这些技术可为几个（平面和非平面）图类（包括有界带宽，完整图和平面图）提供磁盘链接图形的面积要求的上限。特别是，完整图和平面图的呈现边界渐近严格。