APPROXIMATING MINIMUM MAX-STRETCH SPANNING TREES ON UNWEIGHTED GRAPHS
Given a graph G and a spanning tree T of G, we say that T is a tree t-spanner of G if the distance between every pair of vertices in T is at most t times their distance in G. The problem of finding a tree t-spanner minimizing t is referred to as the Minimum Max-Stretch spanning Tree (MMST) problem. This paper concerns the MMST problem on unweighted graphs. The problem is known to be NP-hard, and the paper presents an O(log n)-approximation algorithm for it. Furthermore, it is established that unless P = NP, the problem cannot be approximated additively by any o(n) term.
spanning trees low stretch spanners