An edge-swap heuristic for generating spanning trees with minimum number of branch vertices
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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. (Lect Notes Comput Sci 2380:355–365, 2002) and has been called the minimum branch vertices problem by Cerulli et al. (Comput Optim Appl 42:353–370, 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.
KeywordsConstrained spanning trees Branch vertices Minimum branch vertices problem Heuristic Multi-start heuristic Edge swapping
The research of R.M.A Silva was partially done while he was a post-doc scholar at AT&T Labs Research in Florham Park, New Jersey, and was partially supported by the Brazilian National Council for Scientific and Technological Development (CNPq), the Foundation for Support of Research of the State of Minas Gerais, Brazil (FAPEMIG), Coordination for the Improvement of Higher Education Personnel, Brazil (CAPES), and Foundation for the Support of Development of the Federal University of Pernambuco, Brazil (FADE). José F. Gonçalves was supported by funds granted by the ERDF through the Programme COMPETE and by the Portuguese Government through FCT – Foundation for Science and Technology, project PTDC/EGE-GES/117692/2010. Diego M. Silva was partially supported by CAPES-MINTER Program between the Federal Universities of Minas Gerais and Lavras, Brazil.
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