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» Crossing numbers of random graphs
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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
APPROX
2008
Springer
184views Algorithms» more  APPROX 2008»
13 years 10 months ago
Approximately Counting Embeddings into Random Graphs
Let H be a graph, and let CH(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating CH(G). Previous res...
Martin Fürer, Shiva Prasad Kasiviswanathan
GD
2007
Springer
14 years 2 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
ISCAS
1999
IEEE
95views Hardware» more  ISCAS 1999»
14 years 5 days ago
Evaluating iterative improvement heuristics for bigraph crossing minimization
The bigraph crossing problem, embedding the two node sets of a bipartite graph G = V0;V1;E along two parallel lines so that edge crossings are minimized, has application to placeme...
Matthias F. M. Stallmann, Franc Brglez, Debabrata ...
RSA
2006
81views more  RSA 2006»
13 years 7 months ago
On random points in the unit disk
Let n be a positive integer and > 0 a real number. Let Vn be a set of n points in the unit disk selected uniformly and independently at random. Define G(, n) to be the graph w...
Robert B. Ellis, Xingde Jia, Catherine H. Yan