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» Crossing numbers of random graphs
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COCOON
2006
Springer
15 years 9 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»
15 years 7 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
128
Voted
GD
2007
Springer
15 years 11 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»
15 years 10 months 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»
15 years 5 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