An edge-swap heuristic for generating spanning trees with minimum number of branch vertices

Abstract. This paper presents a new edge-swap heuristic for generating spanning trees with a minimum number of branch vertices, i.e. vertices of degree greater than two. This problem was introduced in Gargano et al. (2002) and has been called the minimum branch vertices (MBV) problem by Cerulli et al. (2009). The heuristic starts with a random spanning tree and iteratively reduces the number of branch vertices by swapping tree edges with edges not currently in the tree. It can be easily implemented as a multi-start heuristic. We report on extensive computational experiments comparing single-start and multi-start variants on our heuristic with other heuristics previously proposed in the literature.