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ESA
2008
Springer
115views Algorithms» more  ESA 2008»
13 years 8 months ago
A New Approach to Exact Crossing Minimization
The crossing number problem is to find the smallest number of edge crossings necessary when drawing a graph into the plane. Eventhough the problem is NP-hard, we are interested in ...
Markus Chimani, Petra Mutzel, Immanuel M. Bomze
ENDM
2008
59views more  ENDM 2008»
13 years 6 months ago
Unexpected behaviour of crossing sequences
The nth crossing number of a graph G, denoted crn(G), is the minimum number of crossings in a drawing of G on an orientable surface of genus n. We prove that for every a > b &g...
Matt DeVos, Bojan Mohar, Robert Sámal
CORR
2010
Springer
162views Education» more  CORR 2010»
13 years 3 months ago
Cross-Composition: A New Technique for Kernelization Lower Bounds
We introduce a new technique for proving kernelization lower bounds, called cross-composition. A classical problem L cross-composes into a parameterized problem Q if an instance o...
Hans L. Bodlaender, Bart M. P. Jansen, Stefan Krat...
JCT
2007
90views more  JCT 2007»
13 years 6 months ago
On the maximum number of edges in quasi-planar graphs
A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [2] proved that these graphs have a linear number of edges. We give a sim...
Eyal Ackerman, Gábor Tardos
WALCOM
2010
IEEE
255views Algorithms» more  WALCOM 2010»
14 years 1 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...