Tree spanners of bounded degree graphs

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...

Spanners of bounded degree graphs

Spanners for bounded tree-length graphs

This paper concerns construction of additive stretched spanners with few edges for n-vertex graphs having a tree-decomposition into bags of diameter at most δ, i.e., the tree-length δ graphs. For such graphs we construct additive 2δ-spanners with O(δn+n log n) edges, and additive 4δ-spanners with O(δn) edges. This provides new upper bounds for chordal graphs for which δ = 1. We also show a lowe...

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...