Optimal Independent Spanning Trees on Hypercubes

Abstract

Two spanning trees rooted at some vertex r in a graph G are said to be independent if for each vertex v of G, v r,the paths from r to v in two trees are vertex-disjoint. A set of spanning trees of G is said to be independent if they are pairwise independent. A set of independent spanning trees is optimal if the average path length of trees is minimum. Any k-dimension hypercube has k independent spanning trees rooted at an abitrary vertex. In this paper, a linear time algorithm is proposed to construct k optimal independent spanning trees on a k-dimension hypercube.