# A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees

In this paper, we present a new bicriteria approximation algorithm for the degreebounded
minimum spanning tree problem. In this problem, we are given an undirected graph, a
nonnegative cost function on the edges, and a positive integer B∗, and the goal is to find a minimumcost
spanning tree T with maximum degree at most B∗. In an n-node graph, our algorithm finds
a spanning tree with maximum degree O(B∗ + log n) and cost O( opt B∗ ), where opt B∗ is the
minimum cost of any spanning tree whose maximum degree is at most B∗. Our algorithm uses ideas
from Lagrangean duality. We show how a set of optimum Lagrangean multipliers yields bounds on
both the degree and the cost of the computed solution.