Additive Spanners Research Articles

An Optimal Disjoint Pair of Additive Spanners for the 3D Grid

A spanner of a connected graph G is a spanning connected subgraph S. If DG(u, v) and DS(u, v) denote the distance between vertices u and v in G and S, respectively, then S is an f(x)-spanner if and only if DS(u, v) ≤ f(DG(u, v)). The value f(x) - x is the delay of the spanner. An additive spanner is one with constant delay. Given a graph G and function f(x), an interesting problem is to partition the edges of G so as to define edge-disjoint f(x)-spanners of G. This paper exhibits a pair of (x + 4)-spanners for the infinite three dimensional grid, and shows that 4 is the least integer K for which there exists an edge-disjoint pair of delay-K spanners. spanner, grid, additive spanner, parallel network.

Additive graph spanners

AbstractA spanning subgraph S = (V, E′) of a connected simple graph G = (V, E) is a f(x)‐spanner if for any pair of nodes u and v, dS(u, v) ≦ f(dG(u, v)), where dG and dS are the usual distance functions in graphs G and S, respectively. We are primarily interested in (t + x)‐spanners, which we refer to as additive spanners. We construct low‐degree additive spanners for X‐trees, pyramids, and multidimensional grids. We prove, for arbitrary t > 0, that to determine whether a given graph G has an additive spanner with no more than m edges is NP‐complete. © 1993 by John Wiley & Sons, Inc.