Grid Drawings of Graphs with Constant Edge-Vertex Resolution

by   Michael A. Bekos, et al.
National Technical University of Athens
University of Cologne
Universität Tübingen
Università Perugia

We study the algorithmic problem of computing drawings of graphs in which (i) each vertex is a disk with constant radius r, (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 edge-vertex resolution is at least r, that is, no edge segment intersects a non-adjacent disk. We call such drawings disk-link drawings. This model is motivated by the fact that common graph editors represent vertices as geometric features (usually either as disks or as squares) of fixed size. In this scenario, vertex-vertex and edge-vertex overlaps cause visual clutter and may generate ambiguities. Since such issues can be solved by scaling up the drawing by a suitable factor, we present constructive techniques that yield more compact upper bounds for the area requirements of disk-link drawings for several (planar and nonplanar) graph classes, including proper level, bounded bandwidth, complete, planar and outerplanar graphs.


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