Independent Tree Spanners

For any fixed parameter t ≥ 1, a tree t-spanner of a graph G is a spanning tree T of G such that the distance between every pair of vertices in T is at most t times their distance in G. In this paper, we incorporate a concept of fault-tolerance by examining independent tree t-spanners. Given a root vertex r, this is a pair of tree t-spanners, such that the two paths from any vertex to r are edge (resp., internally vertex) disjoint. It is shown that a pair of independent tree 2-spanners can be found in linear time, whereas the problem for arbitrary t ≥ 4 is \(\cal NP\)-complete.