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» An Algorithm for the Graph Crossing Number Problem
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SODA
2003
ACM
103views Algorithms» more  SODA 2003»
13 years 8 months ago
On the rectilinear crossing number of complete graphs
We prove a lower bound of 0.3288   n 4¡ for the rectilinear crossing number cr(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadril...
Uli Wagner
WEA
2007
Springer
112views Algorithms» more  WEA 2007»
14 years 1 months ago
Crossing Minimization in Weighted Bipartite Graphs
Given a bipartite graph G = (L0, L1, E) and a fixed ordering of the nodes in L0, the problem of finding an ordering of the nodes in L1 that minimizes the number of crossings has ...
Olca A. Çakiroglu, Cesim Erten, Ömer K...
GD
2007
Springer
14 years 1 months ago
Line Crossing Minimization on Metro Maps
We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V, E), so that the total number of crossings among pairs of paths is m...
Michael A. Bekos, Michael Kaufmann, Katerina Potik...
WALCOM
2010
IEEE
255views Algorithms» more  WALCOM 2010»
14 years 2 months ago
A Global k-Level Crossing Reduction Algorithm
Abstract. Directed graphs are commonly drawn by the Sugiyama algorithm, where crossing reduction is a crucial phase. It is done by repeated one-sided 2-level crossing minimizations...
Christian Bachmaier, Franz-Josef Brandenburg, Wolf...
GD
2009
Springer
13 years 12 months ago
Removing Independently Even Crossings
We show that cr(G) ≤ 2 iocr(G) 2 settling an open problem of Pach and T´oth [4, 1]. Moreover, iocr(G) = cr(G) if iocr(G) ≤ 2. 1 Crossing Numbers Pach and T´oth point out in ...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...