Given a set V of n points in Rd and a real constant t > 1, we present the first O(n log n)-time algorithm to compute a geometric t-spanner on V . A geometric t-spanner on V is a...
Joachim Gudmundsson, Christos Levcopoulos, Giri Na...
We study the cover time of random geometric graphs. Let I(d) = [0, 1]d denote the unit torus in d dimensions. Let D(x, r) denote the ball (disc) of radius r. Let Υd be the volume...
The unit ball random geometric graph G = Gd p(λ, n) has as its vertices n points distributed independently and uniformly in the unit ball in Rd, with two vertices adjacent if and ...
Robert B. Ellis, Jeremy L. Martin, Catherine H. Ya...
We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than w...
We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straightline edges and assign each edge to a lay...
Michael B. Dillencourt, David Eppstein, Daniel S. ...