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» Plane and Planarity Thresholds for Random Geometric Graphs
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COMPGEOM
2006
ACM
13 years 11 months ago
Minimum weight triangulation is NP-hard
A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum weight triangulation (MWT) problem, we are looking for a triangula...
Wolfgang Mulzer, Günter Rote
ALGOSENSORS
2004
Springer
13 years 11 months ago
On a Conjecture Related to Geometric Routing
We conjecture that any planar 3-connected graph can be embedded in the plane in such a way that for any nodes s and t, there is a path from s to t such that the Euclidean distance ...
Christos H. Papadimitriou, David Ratajczak
SODA
2003
ACM
143views Algorithms» more  SODA 2003»
13 years 7 months ago
Matching planar maps
The subject of this paper are algorithms for measuring the similarity of patterns of line segments in the plane, a standard problem in, e.g., computer vision, geographic informati...
Helmut Alt, Alon Efrat, Günter Rote, Carola W...
GD
2007
Springer
13 years 12 months ago
Simultaneous Geometric Graph Embeddings
We consider the following problem known as simultaneous geometric graph embedding (SGE). Given a set of planar graphs on a shared vertex set, decide whether the vertices can be pla...
Alejandro Estrella-Balderrama, Elisabeth Gassner, ...
IM
2008
13 years 5 months ago
Fast and Efficient Restricted Delaunay Triangulation in Random Geometric Graphs
Let G = G(n, r) be a random geometric graph resulting from placing n nodes uniformly at random in the unit square (disk) and connecting every two nodes if and only if their Euclide...
Chen Avin