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|dG(u,v)−dT(u,v)|⩽1. A polynomial time algorithm is designed for finding such a tree.