Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed prox...
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...
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...
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular g...
In the directed acyclic graph (dag) model of algorithms, consider the following problem for precedence-constrained multiprocessor schedules for array computations: Given a sequenc...