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- W4287781410 abstract "We study the algorithmic problem of computing drawings of graphs in which $(i)$ each vertex is a disk with fixed radius $rho$, $(ii)$ 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 emph{edge-vertex resolution}, is at least $rho$. We call such drawings emph{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." @default.
- W4287781410 created "2022-07-26" @default.
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- W4287781410 date "2020-05-05" @default.
- W4287781410 modified "2023-09-29" @default.
- W4287781410 title "Grid Drawings of Graphs with Constant Edge-Vertex Resolution" @default.
- W4287781410 doi "https://doi.org/10.48550/arxiv.2005.02082" @default.
- W4287781410 hasPublicationYear "2020" @default.
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