Embedding 3-polytopes on a small grid

Authors:
Ares Ribó Mor;Günter Rote;André Schulz
Affiliations:
FU Berlin, Berlin, Germany;FU Berlin, Berlin, Germany;FU Berlin, Berlin, Germany
Venue:
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Year:
2007

Citing 3
Cited 2

On the maximal number of edges of convex digital polygons included into an m × m-grid

Journal of Combinatorial Theory Series A
Embedding planar graphs on the grid

SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Convex Drawings of 3-Connected Plane Graphs

Algorithmica

Resolving Loads with Positive Interior Stresses

WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
On the number of spanning trees a planar graph can have

ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show how to embed a 3-connected planar graph with n verticesas a 3-polytope with small integer coordinates.The coordinates are bounded by O(27.55n). The crucial part is the construction of a plane embeddingwhich supports an equilibrium stress.We have to guarantee that the size of the coordinates and thestresses are small.This is achieved by applying Tutte's spring embedding method carefully.