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**1 - 1**of**1**### On the Volume and Resolution of 3-Dimensional Convex Graph Drawing (Extended Abstract)

"... We address the problem of drawing a 3-connected planar graph as a convex polyhedron in R³. We give an efficient algorithm for producing such a realization using O(n) volume under the vertex-resolution rule. Each vertex in the drawing resulting from this method is guaranteed to need no more than O(n ..."

Abstract
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We address the problem of drawing a 3-connected planar graph as a convex polyhedron in R³. We give an efficient algorithm for producing such a realization using O(n) volume under the vertex-resolution rule. Each vertex in the drawing resulting from this method is guaranteed to need no more than O(n log n) bits to represent (as a pair of rational numbers). This solves an open problem of Cohen, Eades, Lin, and Ruskey. We also show that under the angular-resolution rule drawing a 3-connected planar graph as a convex polyhedron in R³ requires at least exponential volume in the worst case.