Name
Abstract | ||
|---|---|---|
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than @p). In this paper we prove that the opposite statement is also true, namely that planar minimally rigid graphs always admit pointed embeddings, even under certain natural topological and combinatorial constraints. The proofs yield efficient embedding algorithms. They also provide the first algorithmically effective result on graph embeddings with oriented matroid constraints other than convexity of faces. These constraints are described by combinatorial pseudo-triangulations, first defined and studied in this paper. Also of interest are our two proof techniques, one based on Henneberg inductive constructions from combinatorial rigidity theory, the other on a generalization of Tutte's barycentric embeddings to directed graphs. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.comgeo.2004.07.003 | Symposium on Computational Geometry |
Keywords | Field | DocType |
combinatorial constraint,pointed vertex,barycentric embeddings,pseudotriangulations,henneberg inductive construction,pointed pseudo-triangulations,combinatorial rigidity theory,rigidity,algorithmically effective result,planar minimally rigid graph,graph drawing,combinatorial pseudo-triangulations,graph embeddings,oriented matroid,graph embedding | Discrete mathematics,Combinatorics,Outerplanar graph,Laman graph,Oriented matroid,Planar straight-line graph,Book embedding,1-planar graph,Topological graph theory,Planar graph,Mathematics | Journal |
Volume | Issue | ISSN |
31 | 1-2 | Computational Geometry: Theory and Applications |
ISBN | Citations | PageRank |
1-58113-663-3 | 49 | 2.67 |
References | Authors | |
32 | 9 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ruth Haas | 1 | 126 | 14.01 |
| David Orden | 2 | 160 | 20.26 |
| Günter Rote | 3 | 1181 | 129.29 |
| Francisco Santos | 4 | 184 | 18.73 |
| Brigitte Servatius | 5 | 141 | 19.37 |
| Herman Servatius | 6 | 99 | 14.35 |
| Diane L. Souvaine | 7 | 480 | 77.99 |
| Ileana Streinu | 8 | 510 | 64.64 |
| Walter Whiteley | 9 | 450 | 32.34 |