A linear-time algorithm for drawing a planar graph on a grid
Information Processing Letters
Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
Theoretical Computer Science
A linear-time algorithm for four-partitioning four-connected planar graphs
Information Processing Letters
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Minimum-width grid drawings of plane graphs
Computational Geometry: Theory and Applications
Convex grid drawings of plane graphs with rectangular contours
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
The approximate rectangle of influence drawability problem
GD'12 Proceedings of the 20th international conference on Graph Drawing
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A convex grid drawing of a plane graph G is a drawing of G on the plane so that all vertices of G are put on grid points, all edges are drawn as straight-line segments between their endpoints without any edge-intersection, and every face boundary is a convex polygon. In this paper we give a linear-time algorithm for finding a convex grid drawing of any 4-connected plane graph G with four or more vertices on the outer face boundary. The algorithm yields a drawing in an integer grid such that W + H ≤ n - 1 if G has n vertices, where W is the width and H is the height of the grid. Thus the area W × H of the grid is at most ⌈(n - 1)/2⌉ ċ ⌊(n - 1)/2⌋. Our bounds on the grid sizes are optimal in the sense that there exist an infinite number of 4-connected plane graphs whose convex drawings need grids such that W + H = n - 1 and W × H = ⌈(n - 1)/2⌉ ċ ⌊(n - 1)/2⌋.