Abstract

We provide O(n)-time algorithms for constructing the following types of drawings of n-vertex 3-connected planar graphs: ffl 2D convex grid drawings with (3n) \Theta (3n=2) area under the edge L1 -resolution rule; ffl 2D strictly convex grid drawings with O(n 3 ) \Theta O(n 3 ) area under the edge resolution rule; ffl 2D strictly convex drawings with O(1) \Theta O(n) area under the vertex-resolution rule, and with vertex coordinates represented by O(n log n)-bit rational numbers; ffl 3D convex drawings with O(1) \Theta O(1) \Theta O(n) volume under the vertex-resolution rule, and with vertex coordinates represented by O(n log n)-bit rational numbers. We also show the following lower bounds: ffl For infinitely many n-vertex graphs G, if G has a straightline 2D convex drawing in a w \Theta h grid satisfying the edge L1 -resolution rule then w;h 5n=6 +\Omega\Gamma20 and w + h 8n=3 + \Omega\Gamma838 ffl For infinitely many bounded-degree triconnected planar graphs G with n ver...

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