Finding Multiple Redundant Trees in Linear Time

Abstract

Redundant trees are directed spanning trees, which provide disjoint paths towards their roots. Therefore, this concept is widely applied in the literature both for providing protection and load sharing. The fastest algorithm can find multiple redundant trees, a pair of them rooted at each vertex, in linear time. Unfortunately, edge- or vertex-redundant trees can only be found in 2-edge- or 2-vertex-connected graphs respectively. Therefore, the concept of maximally redundant trees was introduced, which can overcome this problem, and provides maximally disjoint paths towards the common root. In this paper, we propose the first linear time algorithm, which can compute a pair of maximally redundant trees rooted at not only one, but at each vertex.