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;...
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...
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...
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...
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...