Additive graph spanners
Arthur L. Liestman, Thomas Caton Shermer · Networks · 1993
Abstract A 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.