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» Bidimensionality and geometric graphs
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SAC
2006
ACM
14 years 1 months ago
Spatial geometric constraint solving based on k-connected graph decomposition
We propose a geometric constraint solving method based on connectivity analysis in graph theory, which can be used to decompose a well-constrained problem into some smaller ones i...
Gui-Fang Zhang, Xiao-Shan Gao
COMGEO
2008
ACM
13 years 7 months ago
Augmenting the connectivity of geometric graphs
Let G be a connected plane geometric graph with n vertices. In this paper, we study bounds on the number of edges required to be added to G to obtain 2-vertex or 2-edge connected ...
Manuel Abellanas, Alfredo García Olaverri, ...
CORR
2008
Springer
133views Education» more  CORR 2008»
13 years 7 months ago
On Geometric Spanners of Euclidean and Unit Disk Graphs
We consider the problem of constructing bounded-degree planar geometric spanners of Euclidean and unit-disk graphs. It is well known that the Delaunay subgraph is a planar geometri...
Iyad A. Kanj, Ljubomir Perkovic
GD
2006
Springer
13 years 11 months ago
Computing Geometric Minimum-Dilation Graphs Is NP-Hard
We prove that computing a geometric minimum-dilation graph on a given set of points in the plane, using not more than a given number of edges, is an NP-hard problem, no matter if ...
Rolf Klein, Martin Kutz
COMBINATORICA
2008
88views more  COMBINATORICA 2008»
13 years 7 months ago
Geometric graphs with no two parallel edges
We give a simple proof for a theorem of Katchalski, Last, and Valtr, asserting that the maximum number of edges in a geometric graph G on n vertices with no pair of parallel edges...
Rom Pinchasi