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COMPGEOM
1996
ACM

Convex Drawings of Graphs in Two and Three Dimensions (Preliminary Version)

9 years 6 months ago
Convex Drawings of Graphs in Two and Three Dimensions (Preliminary Version)
We provideO(n)-timealgorithmsfor constructingthe following types of drawings of n-vertex 3-connectedplanar graphs: 2D convex grid drawings with (3n) (3n=2) area under the edge L1-resolution rule; 2D strictly convex grid drawings with O(n 3) O(n 3) area under the edge resolution rule; 2D strictly convex drawings with O(1) O(n) area under the vertex-resolution rule, and with vertex coordinates represented by O(n logn)-bit rational numbers; 3D convex drawings with O(1) O(1) O(n) volume under the vertex-resolution rule, and with vertex coordinates represented by O(n logn)-bit rational numbers. We also show the following lower bounds: For in nitely many n-vertex graphs G, if G has a straightline 2D convex drawing in a w h grid satisfying the edge L1-resolution rule then w; h 5n=6 + (1) and w + h 8n=3+ (1). For in nitely many bounded-degree triconnected planar graphs G with n vertices, any 3D convex drawing of G must have volume 2 (n) under the angular resolution rule.
Marek Chrobak, Michael T. Goodrich, Roberto Tamass
Added 08 Aug 2010
Updated 08 Aug 2010
Type Conference
Year 1996
Where COMPGEOM
Authors Marek Chrobak, Michael T. Goodrich, Roberto Tamassia
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