Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Convex drawings of graphs in two and three dimensions (preliminary version)
Proceedings of the twelfth annual symposium on Computational geometry
On the complexity of optimization problems for 3-dimensional convex polyhedra and decision trees
Computational Geometry: Theory and Applications
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Drawing Stressed Planar Graphs in Three Dimensions
GD '95 Proceedings of the Symposium on Graph Drawing
Discrete one-forms on meshes and applications to 3D mesh parameterization
Computer Aided Geometric Design
Embedding stacked polytopes on a polynomial-size grid
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We study the problem how to obtain a small drawing of a 3-polytope with Euclidean distance between any two points at least 1. The problem can be reduced to a one-dimensional problem, since it is sufficient to guarantee distinct integer x-coordinates. We develop an algorithm that yields an embedding with the desired property such that the polytope is contained in a 2(n−2)×1 ×1 box. The constructed embedding can be scaled to a grid embedding whose x-coordinates are contained in [0,2(n−2)]. Furthermore, the point set of the embedding has a small spread, which differs from the best possible spread only by a multiplicative constant.