An exact algorithm for the maximum leaf spanning tree problem

Abstract

Given a connected graph, the Maximum Leaf Spanning Tree Problem (MLSTP) is to find a spanning tree whose number of leaves (degree-one vertices) is maximum. We propose a branch-and-bound algorithm for MLSTP, in which an upper bound is obtained by solving a minimum spanning tree problem. We report computational results for randomly generated graphs and grid graphs with up to 100 vertices. Scope and purpose There exist many applications which can be modeled using graphs. Spanning trees in a graph are often considered since it consists of the minimal set of edges which connect each pair of vertices. The minimum spanning tree problem is a classical and fundamental problem on graphs. In this paper, we consider the maximum leaf spanning tree problem which is to find a spanning tree with the maximum number of leaves (degree-one vertices). This problem has an application in the area of communication networks and circuit layouts. Since the problem is NP-hard, several approximation algorithms have been considered. The purpose of the paper is to propose a branch-and-bound algorithm for the problem. We propose an upper bound which is obtained by solving the minimum spanning tree problem. To the author's knowledge, this is the first exact algorithm to the problem.