The Directed Minimum-Degree Spanning Tree Problem

Consider a directed graph G = (V,E) with n vertices and a root vertex r ∈ V . The DMDST problem for G is one of constructing a spanning tree rooted at r, whose maximal degree is the smallest among all such spanning trees. The problem is known to be NP-hard. A quasipolynomial time approximation algorithm for this problem is presented. The algorithm finds a spanning tree whose maximal degree is at most O(∆∗ + log n) where, ∆∗ is the degree of some optimal tree for the problem. The running time of the algorithm is shown to be O(n). Experimental results are presented showing that the actual running time of the algorithm is much smaller in practice.