Bounded-Degree Plane Geometric Spanners in Practice

On bounded degree plane strong geometric spanners

Article history: Received 13 October 2010 Received in revised form 18 March 2012 Accepted 19 March 2012 Available online xxxx

Bounded Degree Planar Geometric Spanners

Given a set P of n points in the plane, we show how to compute in O(n logn) time a subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong planar t-spanner of P with t = (1 + √ 2) ∗ δ, where δ is the spanning ratio of the Delaunay triangulation. Furthermore, given a Delaunay triangulation, we show a distributed algorithm that computes the same bounded degree planar sp...

On Plane Constrained Bounded-Degree Spanners

Let P be a finite set of points in the plane and S a set of non-crossing line segments with endpoints in P . The visibility graph of P with respect to S, denoted Vis(P, S), has vertex set P and an edge for each pair of vertices u, v in P for which no line segment of S properly intersects uv. We show that the constrained half-θ6-graph (which is identical to the constrained Delaunay graph whose e...

Plane Geometric Spanners

Let S be a set of n points in the plane and let G be an undirected graph with vertex set S, in which each edge (u, v) has a weight, which is equal to the Euclidean distance |uv| between the points u and v. For any two points p and q in S, we denote their shortest-path distance in G by δG(p, q). If t ≥ 1 is a real number, then we say that G is a t-spanner for S if δG(p, q) ≤ t|pq| for any two po...

Spanners of bounded degree graphs