Bounded Degree Spanners of the Hypercube

Spanners of bounded degree graphs

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...

Diamond Triangulations Contain Spanners of Bounded Degree

Given a triangulation G, whose vertex set V is a set of n points in the plane, and given a real number γ with 0 < γ < π, we design an O(n)-time algorithm that constructs a connected spanning subgraph G′ of G whose maximum degree is at most 14 + d2π/γe. If G is the Delaunay triangulation of V , and γ = 2π/3, we show that G′ is a t-spanner of V (for some constant t) with maximum degree at most 17...

Tree spanners of bounded degree graphs

A tree t-spanner of a graph G is a spanning tree of G such that the distance between pairs of vertices in the tree is at most t times their distance in G. Deciding tree t-spanner admissible graphs has been proved to be tractable for t < 3 and NP-complete for t > 3, while the complexity status of this problem is unresolved when t = 3. For every t > 2 and b > 0, an efficient dynamic programming a...

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...