Convex grid drawings of planar graphs with constant edge-vertex resolution

In this work, we continue the study of the area required for convex straight-line grid drawings of 3-connected plane graphs, which has been intensively investigated in the last decades. Motivated by applications, such as graph editors, we additionally require the obtained drawings to have bounded edge-vertex resolution, that is, the closest distance between a vertex and any non-incident edge in the drawing is lower bounded by a constant that does not depend on the size of the graph. We present a drawing algorithm that takes as input a 3-connected plane graph with.. vertices and f internal faces, and computes a convex straight-line drawing with edge-vertex resolution at least 1/2 on an integer grid of size (n - 2 + a) x (n - 2 + a), where a = min{n - 3, f}. Our result improves the previously best-known area bound of (3n - 7) x (3n - 7)/2 by Chrobak, Goodrich and Tamassia.