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An approach for the Steiner problem in directed graphs

  • Section VI Steiner Tree Networks
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Abstract

We present a scheme to solve the Steiner problem in directed graphs using a heuristic method to obtain upper bounds and thek shortest arborescences algorithm to compute lower bounds. We propose to combine these ideas in an enumerative algorithm. Computational results are presented for both thek shortest arborescences algorithm and the heuristic method, including reduction tests for the problem.

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References

  1. A. Balakrishnan and N. Patel, Problem reduction methods and a tree generation algorithm for the Steiner network problem, Networks 17(1987)65–85.

    Google Scholar 

  2. J.E. Beasley, An algorithm for the Steiner problem in graphs, Networks 14(1984)147–159.

    Google Scholar 

  3. J.E. Beasley, An SST-based algorithm for the Steiner problem in graphs, Networks 19(1989)1–16.

    Google Scholar 

  4. P. Camerini, L. Fratta and F. Maffioli, Thek best spanning arborescences of a network, Networks 10(1980)91–110.

    Google Scholar 

  5. A. Candia, P. Souza and N. Maculan, Reduction tests for the Steiner problem in directed graphs, Working Paper.

  6. M. Dror, B. Gavish and J. Choquette, Directed Steiner tree problem on a graph: Models, relaxations and algorithms, Technical Report, Centre de Recherche sur les Transports, Université de Montréal, Canada (1988).

    Google Scholar 

  7. C. Duin and A. Volgenant, Reduction tests for the Steiner problem in graphs, Networks 19(1989)549–567.

    Google Scholar 

  8. W. Liu, Extended formulation and polyhedral projection, Ph.D. Thesis, Department of Combinatorics and Optimization, University of Waterloo, Canada (1988).

    Google Scholar 

  9. N. Maculan, The Steiner problem in graphs, Ann. Discr. Math. 31(1987)185–212.

    Google Scholar 

  10. O.I. Palma-Pacheco, Contribuição para a resolução do problema de Steiner num grafo direcionado: um método heurístico, Ph.D. Thesis, Systems Engineering and Computer Sciences, COPPE, Federal University of Rio de Janeiro, Brazil (1985).

    Google Scholar 

  11. O.I. Palma-Pacheco and N. Maculan, Método heurístico para o problema de Steiner num grafo direcionado,Proc. 3rd Latin American Conf. on Operations Research and Systems Engineering, Vol. 1, Santiago, Chile (1986), pp. 117–141.

  12. P. Winter, The Steiner problem in networks — A survey, Networks 17(1987)129–167.

    Google Scholar 

  13. R.T. Wong, A dual ascent approach for Steiner tree problems on a directed graph, Math. Progr. 28(1984)271–287.

    Google Scholar 

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This work was partially supported by CNPq, FINEP, CAPES and IBM do Brasil.

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Maculan, N., Souza, P. & Candia Vejar, A. An approach for the Steiner problem in directed graphs. Ann Oper Res 33, 471–480 (1991). https://doi.org/10.1007/BF02071983

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  • DOI: https://doi.org/10.1007/BF02071983

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