208 search results - page 3 / 42 » Improved upper bounds on the crossing number |
COMPGEOM
1996
ACM
13 years 9 months ago
1996
ACM
Given a simple arrangementof n pseudolines in the Euclidean plane, associate with line i the list i of the lines crossing i in the order of the crossings on line i. i = ( i 1; i 2;...
SAT
2005
Springer
13 years 10 months ago
2005
Springer
We give a randomized algorithm for testing satisfiability of Boolean formulas in conjunctive normal form with no restriction on clause length. Its running time is at most 2n(1−1...
JCT
2007
13 years 4 months ago
2007
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...
FOCS
2006
IEEE
13 years 11 months ago
2006
IEEE
We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most in an arrangement of n halfspaces in Rd , for arbitrary n and d (in particular, the...
SODA
2010
ACM
14 years 2 months ago
2010
ACM
The crossing number of a graph is the least number of pairwise edge crossings in a drawing of the graph in the plane. We provide an O(n log n) time constant factor approximation al...