Artículos de revistas
Reformulations And Solution Algorithms For The Maximum Leaf Spanning Tree Problem
Registro en:
Computational Management Science. , v. 7, n. 3, p. 289 - 311, 2010.
1619697X
10.1007/s10287-009-0116-5
2-s2.0-77954087471
Autor
Lucena A.
Maculan N.
Simonetti L.
Institución
Resumen
Given a graph G = (V, E), the maximum leaf spanning tree problem (MLSTP) is to find a spanning tree of G with as many leaves as possible. The problem is easy to solve when G is complete. However, for the general case, when the graph is sparse, it is proven to be NP-hard. In this paper, two reformulations are proposed for the problem. The first one is a reinforced directed graph version of a formulation found in the literature. The second recasts the problem as a Steiner arborescence problem over an associated directed graph. Branch-and-Cut algorithms are implemented for these two reformulations. Additionally, we also implemented an improved version of a MLSTP Branch-and-Bound algorithm, suggested in the literature. All of these algorithms benefit from pre-processing tests and a heuristic suggested in this paper. Computational comparisons between the three algorithms indicate that the one associated with the first reformulation is the overall best. It was shown to be faster than the other two algorithms and is capable of solving much larger MLSTP instances than previously attempted in the literature. © 2010 Springer-Verlag. 7 3 289 311 Aneja, Y.P., An integer linear programming approach to the Steiner problem in graphs (1980) Networks, 10, pp. 167-178 Chopra, S., Gorres, E., Rao, M.R., Solving Steiner tree problem on a graph using branch and cut (1992) ORSA J Comput, 4 (3), pp. 320-335 Edmonds, J., Matroids and the greedy algorithm (1971) Math Prog, 1, pp. 127-136 Fernandes, M.L., Gouveia, L., Minimal spanning trees with a constraint on the number of leaves (1998) Eur J Oper Res, 104, pp. 250-261 Fujie, T., An exact algorithm for the maximum-leaf spanning tree problem (2003) Comput Oper Res, 30, pp. 1931-1944 Fujie, T., The maximum-leaf spanning tree problem: Formulations and facets (2004) Networks, 43 (4), pp. 212-223 Galbiati, G., Maffioli, F., Morzenti, A., A short note on the approximability of the maximum leaves spanning tree problem (1994) Info Proc Lett, 52, pp. 45-49 Garey, M.R., Johnson, D.S., (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness, , New York: W. H. Freeman Guha, S., Khuller, S., Approximation algorithms for connected dominating sets (1998) Algorithmica, 20 (4), pp. 374-387 Koch, T., Martin, A., Solving Steiner tree problems in graphs to optimality (1998) Networks, 33, pp. 207-232 Lu, H., Ravi, R., Approximating maximum leaf spanning trees in almost linear time (1998) J Algo, 29, pp. 132-141 Poggi de Aragão, M., Uchoa, E., Werneck, R., Dual heuristics on the exact solution of large Steiner problems (2001) Electron Notes Discret Math, 7, pp. 150-153 Polzin, T., Daneshmand, S.V., Improved algorithms for the Steiner problem in networks (2001) Discret Appl Math, 112 (1-3), pp. 263-300 Resende, M.G.C., Pardalos, P.M., (2006) Handbook of Optimization in Telecommunications, , New York: Springer Solis-Oba, S., 2-approximation algorithm for finding a spanning tree with maximum number of leaves (1998) Lect Notes Comput Sci, 1461, pp. 441-452 Wong, R., A dual ascent approach for Steiner tree problems on a directed graph (1984) Math Prog, 28, pp. 271-287