Delegate and Conquer: An LP-Based Approximation Algorithm for Minimum Degree MSTs

In this paper, we study the minimum degree minimum spanning tree problem: Given a graph G = (V,E) and a non-negative cost function c on the edges, the objective is to find a minimum cost spanning tree T under the cost function c such that the maximum degree of any node in T is minimized. We obtain an algorithm which returns an MST of maximum degree at most Δ∗+k where Δ∗ is the minimum maximum degree of any MST and k is the distinct number of costs in any MST of G. We use a lower bound given by a linear programming relaxation to the problem and strengthen known graph-theoretic results on minimum degree subgraphs [3,5] to prove our result. Previous results for the problem [1,4] used a combinatorial lower bound which is weaker than the LP bound we use