A distance approximating trees
A 1-approximation  of connected graph G=(V,E) G = ( V , E ) is a tree T=(V,E?) T = ( V , E ? ) with the same vertex set such that for every two vertices |dG(u,v)?dT(u,v)|?1 | d G ( u , v ) ? d T ( u , v ) | ? 1 . A polynomial time algorithm is designed for finding such a tree.
distance approximating trees tree spanner