Solving Degree-constrained Minimum Spanning Tree with a New Algorithm

Abstract

The minimum spanning tree (MST) of a graph defines the cheapest subset of edges that keeps the graph in one connected component which is a classic problem in operational research (OR) with important applications in network design. The degree-constrained minimum spanning tree (DCMST) is a special case of MST, which is also an important problem in network design. It consists of finding a spanning tree whose nodes do not exceed a given maximum degree and whose total edge length is minimum. It is known that computing the DCMST is NP-hard. We design a new algorithm for DCMST. At first, the algorithm employs the properties of the problem to remove the pendant vertexes (vertexes of degree 1) from the graph. Then by adding edges to an empty graph in a setting order, the algorithm gets a tree satisfying all the constraints of DCMST. Finally, a better solution comes into being by swapping the edges. This paper also gives an example to demonstrate the principle and the process of the algorithm.