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GD
2007
Springer
14 years 1 months ago
A Bipartite Strengthening of the Crossing Lemma
Let G = (V, E) be a graph with n vertices and m ≥ 4n edges drawn in the plane. The celebrated Crossing Lemma states that G has at least Ω(m3 /n2 ) pairs of crossing edges; or ...
Jacob Fox, János Pach, Csaba D. Tóth
COCOON
2006
Springer
13 years 11 months ago
Fixed Linear Crossing Minimization by Reduction to the Maximum Cut Problem
Many real-life scheduling, routing and location problems can be formulated as combinatorial optimization problems whose goal is to find a linear layout of an input graph in such a ...
Christoph Buchheim, Lanbo Zheng
COMPGEOM
2000
ACM
13 years 11 months ago
When crossings count - approximating the minimum spanning tree
We present an (1+ε)-approximation algorithm for computing the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings betwee...
Sariel Har-Peled, Piotr Indyk
APVIS
2004
13 years 8 months ago
Optimal Leaf Ordering for Two and a Half Dimensional Phylogenetic Tree Visualisation
Two and a half dimensional graph visualisation is the stacking of a set of related graphs into the third dimension to support visual comparison. A new aesthetic criterion is intro...
Tim Dwyer, Falk Schreiber
ENDM
2007
106views more  ENDM 2007»
13 years 7 months ago
Removing Even Crossings on Surfaces
In this paper we investigate how certain results related to the HananiTutte theorem can be extended from the plane to surfaces. We give a simple topological proof that the weak Ha...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...