We consider additive spanners of unweighted undirected graphs. Let G be a
graph and H a subgraph of G. The most na\"ive way to construct an additive
k-spanner of G is the following: As long as H is not an additive
k-spanner repeat: Find a pair (u,v)∈H that violates the
spanner-condition and a shortest path from u to v in G. Add the edges of
this path to H.
We show that, with a very simple initial graph H, this na\"ive method gives
additive 6- and 2-spanners of sizes matching the best known upper bounds.
For additive 2-spanners we start with H=∅ and end with O(n3/2)
edges in the spanner. For additive 6-spanners we start with H containing
⌊n1/3⌋ arbitrary edges incident to each node and end with a
spanner of size O(n4/3).Comment: To appear at proceedings of the 14th Scandinavian Symposium and
Workshop on Algorithm Theory (SWAT 2014