Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Problémes de conception de réseaux

  • Chapter
Optimisation combinatoire

Part of the book series: Collection IRIS ((IRIS))

  • 647 Accesses

Résumé

La connexité est une notion trés importante de l’optimisation combinatoire. Au chapitre 8, nous avons montré comment calculer la connexité entre chaque paire de sommets d’un graphe non orienté. Nous recherchons maintenant des sous-graphes qui vérifient certaines conditions de connexité. Le probléme général est le suivant:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Références

Littérature générale

  • Cheng, X., Du, D.-Z. [2001]: Steiner Trees in Industry. Kluwer, Dordrecht 2001

    Google Scholar 

  • Du, D.-Z., Smith, J.M., Rubinstein, J.H. [2000]: Advances in Steiner Trees. Kluwer, Boston 2000

    MATH  Google Scholar 

  • Hwang, F.K., Richards, D.S., Winter, P. [1992]: The Steiner Tree Problem; Annals of Discrete Mathematics 53. North-Holland, Amsterdam 1992

    MATH  Google Scholar 

  • Goemans, M.X., Williamson, D.P. [1996]: The primal-dual method for approximation algorithms and its application to network design problems. In: Approximation Algorithms for NP-Hard Problems. (D.S. Hochbaum, ed.), PWS, Boston, 1996

    Google Scholar 

  • Grötschel, M., Monma, C.L., Stoer, M. [1995]: Design of survivable networks. In: Handbooks in Operations Research and Management Science; Volume 7; Network Models (M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser, eds.), Elsevier, Amsterdam 1995

    Google Scholar 

  • Kerivin, H., Mahjoub, A.R. [2005]: Design of survivable networks: a survey. Networks 46 (2005), 1–21

    Article  MATH  MathSciNet  Google Scholar 

  • Prömel, H.J., Steger, A. [2002]: The Steiner Tree Problem. Vieweg, Braunschweig 2002

    MATH  Google Scholar 

  • Stoer, M. [1992]: Design of Survivable Networks. Springer, Berlin 1992

    MATH  Google Scholar 

  • Vazirani, V.V. [2001]: Approximation Algorithms. Springer, Berlin 2001, Chapters 22 and 23

    Google Scholar 

Références citées

  • Agrawal, A., Klein, P.N., Ravi, R. [1995]: When trees collide: an approximation algorithm for the generalized Steiner tree problem in networks. SIAM Journal on Computing 24 (1995), 440–456

    Article  MATH  MathSciNet  Google Scholar 

  • Arora, S. [1998]: Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. Journal of the ACM 45 (1998), 753–782

    Article  MATH  MathSciNet  Google Scholar 

  • Berman, P., Ramaiyer, V. [1994]: Improved approximations for the Steiner tree problem. Journal of Algorithms 17 (1994), 381–408

    Article  MATH  MathSciNet  Google Scholar 

  • Bern, M., Plassmann, P. [1989]: The Steiner problem with edge lengths 1 and 2. Information Processing Letters 32 (1989), 171–176

    Article  MATH  MathSciNet  Google Scholar 

  • Bertsimas, D., Teo, C. [1995]: From valid inequalities to heuristics: a unified view of primaldual approximation algorithms in covering problems. Operations Research 46 (1998), 503–514

    Article  MathSciNet  Google Scholar 

  • Bertsimas, D., Teo, C. [1997]: The parsimonious property of cut covering problems and its applications. Operations Research Letters 21 (1997), 123–132

    Article  MATH  MathSciNet  Google Scholar 

  • Borchers, A., Du, D.-Z. [1997]: The k-Steiner ratio in graphs. SIAM Journal on Computing 26 (1997), 857–869

    Article  MATH  MathSciNet  Google Scholar 

  • Borradaile, G., Kenyon-Mathieu, C., Klein, P. [2007]: A polynomial-time approximation scheme for Steiner tree in planar graphs. Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (2007), 1285–1294

    Google Scholar 

  • Cheriyan, J., Vetta, A. [2007]: Approximation algorithms for network design with metric costs. SIAM Journal on Discrete Mathematics 21 (2007), 612–636

    Article  MATH  MathSciNet  Google Scholar 

  • Choukhmane, E. [1978]: Une heuristique pour le probléme de l’arbre de Steiner. RAIRO Recherche Opérationnelle 12 (1978), 207–212 [in French]

    MATH  MathSciNet  Google Scholar 

  • Clementi, A.E.F., Trevisan, L. [1999]: Improved non-approximability results for minimum vertex cover with density constraints. Theoretical Computer Science 225 (1999), 113–128

    Article  MATH  MathSciNet  Google Scholar 

  • Dreyfus, S.E., Wagner, R.A. [1972]: The Steiner problem in graphs. Networks 1 (1972), 195–207

    Article  MATH  MathSciNet  Google Scholar 

  • Du, D.-Z., Zhang, Y., Feng, Q. [1991]: On better heuristic for Euclidean Steiner minimum trees. Proceedings of the 32nd Annual Symposium on the Foundations of Computer Science (1991), 431–439

    Google Scholar 

  • Erickson, R.E., Monma, C.L., Veinott, A.F., Jr. [1987]: Send-and-split method for minimum concave-cost network flows. Mathematics of Operations Research 12 (1987), 634–664

    Article  MATH  MathSciNet  Google Scholar 

  • Fleischer, L., Jain, K., Williamson, D.P. [2006]: Iterative rounding 2-approximation algorithms minimum-cost vertex connectivity problems. Journal of Computer and System Sciences 72 (2006), 838–867

    Article  MATH  MathSciNet  Google Scholar 

  • Fuchs, B., Kern, W., Mölle, D., Richter, S., Rossmanith, P., Wang, X. [2007]: Dynamic programming for minimum Steiner trees. Theory of Computing Systems 41 (2007), 493–500

    Article  MATH  MathSciNet  Google Scholar 

  • Gabow, H.N. [2005]: An improved analysis for approximating the smallest k-edge connected spanning subgraph of a multigraph. SIAM Journal on Discrete Mathematics 19 (2005), 1–18

    Article  MATH  MathSciNet  Google Scholar 

  • Gabow, H.N., Goemans, M.X., Williamson, D.P. [1998]: An efficient approximation algorithm for the survivable network design problem. Mathematical Programming B 82 (1998), 13–40

    MathSciNet  Google Scholar 

  • Gabow, H.N., Goemans, M.X., Tardos, É., Williamson, D.P. [2005]: Approximating the smallest k-edge connected spanning subgraph by LP-rounding. Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (2005), 562–571

    Google Scholar 

  • Garey, M.R., Graham, R.L., Johnson, D.S. [1977]: The complexity of computing Steiner minimal trees. SIAM Journal of Applied Mathematics 32 (1977), 835–859

    Article  MATH  MathSciNet  Google Scholar 

  • Garey, M.R., Johnson, D.S. [1977]: The rectilinear Steiner tree problem is NP-complete. SIAM Journal on Applied Mathematics 32 (1977), 826–834

    Article  MATH  MathSciNet  Google Scholar 

  • Gilbert, E.N., Pollak, H.O. [1968]: Steiner minimal trees. SIAM Journal on Applied Mathematics 16 (1968), 1–29

    Article  MATH  MathSciNet  Google Scholar 

  • Goemans, M.X., Bertsimas, D.J. [1993]: Survivable networks, linear programming and the parsimonious property, Mathematical Programming 60 (1993), 145–166

    Article  MathSciNet  Google Scholar 

  • Goemans, M.X., Goldberg, A.V., Plotkin, S., Shmoys, D.B., Tardos, É., Williamson, D.P. [1994]: Improved approximation algorithms for network design problems. Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms (1994), 223–232

    Google Scholar 

  • Goemans, M.X., Williamson, D.P. [1995]: A general approximation technique for constrained forest problems. SIAM Journal on Computing 24 (1995), 296–317

    Article  MATH  MathSciNet  Google Scholar 

  • Gröpl, C., Hougardy, S., Nierhoff, T., Prömel, H.J. [2001]: Approximation algorithms for the Steiner tree problem in graphs. In: Cheng Du [2001], pp. 235–279

    Google Scholar 

  • Hanan, M. [1966]: On Steiner’s problem with rectilinear distance. SIAM Journal on Applied Mathematics 14 (1966), 255–265

    Article  MATH  MathSciNet  Google Scholar 

  • Hetzel, A. [1995]: Verdrahtung im VLSI-Design: Spezielle Teilprobleme und ein sequentielles Lösungsverfahren. Ph.D. thesis, University of Bonn, 1995 [in German]

    Google Scholar 

  • Hougardy, S., Prömel, H.J. [1999]: A 1:598 approximation algorithm for the Steiner tree problem in graphs. Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (1999), 448–453

    Google Scholar 

  • Hwang, F.K. [1976]: On Steiner minimal trees with rectilinear distance. SIAM Journal on Applied Mathematics 30 (1976), 104–114

    Article  MATH  MathSciNet  Google Scholar 

  • Jain, K. [2001]: A factor 2 approximation algorithm for the generalized Steiner network problem. Combinatorica 21 (2001), 39–60

    Article  MATH  MathSciNet  Google Scholar 

  • Jothi, R., Raghavachari, B., Varadarajan, S. [2003]: A 5/4-approximation algorithm for minimum 2-edge-connectivity. Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (2003), 725–734

    Google Scholar 

  • Karp, R.M. [1972]: Reducibility among combinatorial problems. In: Complexity of Computer Computations (R.E. Miller, J.W. Thatcher, eds.), Plenum Press, New York 1972, pp. 85–103

    Google Scholar 

  • Karpinski, M., Zelikovsky, A. [1997]: New approximation algorithms for Steiner tree problems. Journal of Combinatorial Optimization 1 (1997), 47–65

    Article  MATH  MathSciNet  Google Scholar 

  • Khuller, S., Raghavachari, B. [1996]: Improved approximation algorithms for uniform connectivity problems. Journal of Algorithms 21 (1996), 434–450

    Article  MATH  MathSciNet  Google Scholar 

  • Khuller, S., Vishkin, U. [1994]: Biconnectivity augmentations and graph carvings. Journal of the ACM 41 (1994), 214–235

    Article  MATH  MathSciNet  Google Scholar 

  • Klein, P.N., Ravi, R. [1993]: When cycles collapse: a general approximation technique for constrained two-connectivity problems. Proceedings of the 3rd Integer Programming and Combinatorial Optimization Conference (1993), 39–55

    Google Scholar 

  • Korte, B., Prömel, H.J., Steger, A. [1990]: Steiner trees in VLSI-layout. In: Paths, Flows, and VLSI-Layout (B. Korte, L. Lovász, H.J. Prömel, A. Schrijver, eds.), Springer, Berlin 1990, pp. 185–214

    Google Scholar 

  • Kortsarz, G., Krauthgamer, R., Lee, J.R. [2004]: Hardness of approximation for vertexconnectivity network design problems. SIAM Journal on Computing 33 (2004), 704–720

    Article  MATH  MathSciNet  Google Scholar 

  • Kou, L. [1990]: A faster approximation algorithm for the Steiner problem in graphs. Acta Informatica 27 (1990), 369–380

    Article  MATH  MathSciNet  Google Scholar 

  • Kou, L., Markowsky, G., Berman, L. [1981]: A fast algorithm for Steiner trees. Acta Informatica 15 (1981), 141–145

    Article  MATH  MathSciNet  Google Scholar 

  • Martin, A. [1992]: Packen von Steinerbäumen: Polyedrische Studien und Anwendung. Ph.D. thesis, Technical University of Berlin 1992 [in German]

    Google Scholar 

  • Mehlhorn, K. [1988]: A faster approximation algorithm for the Steiner problem in graphs. Information Processing Letters 27 (1988), 125–128

    Article  MATH  MathSciNet  Google Scholar 

  • Melkonian, V., Tardos, É. [2004]: Algorithms for a network design problem with crossing supermodular demands. Networks 43 (2004), 256–265

    Article  MATH  MathSciNet  Google Scholar 

  • Robins, G., Zelikovsky, A. [2005]: Tighter bounds for graph Steiner tree approximation. SIAM Journal on Discrete Mathematics 19 (2005), 122–134

    Article  MATH  MathSciNet  Google Scholar 

  • Takahashi, M., Matsuyama, A. [1980]: An approximate solution for the Steiner problem in graphs. Mathematica Japonica 24 (1980), 573–577

    MATH  MathSciNet  Google Scholar 

  • Thimm, M. [2003]: On the approximability of the Steiner tree problem. Theoretical Computer Science 295 (2003), 387–402

    Article  MATH  MathSciNet  Google Scholar 

  • Warme, D.M., Winter, P., Zachariasen, M. [2000]: Exact algorithms for plane Steiner tree problems: a computational study. In: Advances in Steiner trees (D.-Z. Du, J.M. Smith, J.H. Rubinstein, eds.), Kluwer Academic Publishers, Boston, 2000, pp. 81–116

    Google Scholar 

  • Williamson, D.P., Goemans, M.X., Mihail, M., Vazirani, V.V. [1995]: A primal-dual approximation algorithm for generalized Steiner network problems. Combinatorica 15 (1995), 435–454

    Article  MATH  MathSciNet  Google Scholar 

  • Zelikovsky, A.Z. [1993]: An 11/6-approximation algorithm for the network Steiner problem. Algorithmica 9 (1993), 463–470

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute for Discrete Mathematics, University of Bonn, Lennéstraße 2, 53113, Bonn, Germany

    Bernhard Korte & Jens Vygen

  2. Faculté de mathématiques, Université Paris-VI, 175, rue du Chevaleret, 75013, Paris

    Jean Fonlupt (Professeur émérite)

  3. Panthéon-Sorbonne Centre d’économie de la Sorbonne, Université Paris-I, 106-112, boulevard de l’Hôpital, 75013, Paris

    Alexandre Skoda

Authors
  1. Bernhard Korte
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jens Vygen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jean Fonlupt
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alexandre Skoda
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag France

About this chapter

Cite this chapter

Korte, B., Vygen, J., Fonlupt, J., Skoda, A. (2010). Problémes de conception de réseaux. In: Optimisation combinatoire. Collection IRIS. Springer, Paris. https://doi.org/10.1007/978-2-287-99037-3_20

Download citation

  • DOI: https://doi.org/10.1007/978-2-287-99037-3_20

  • Publisher Name: Springer, Paris

  • Print ISBN: 978-2-287-99036-6

  • Online ISBN: 978-2-287-99037-3

Publish with us

Policies and ethics

Search

Navigation