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Network Design Problems

NDP

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Encyclopedia of Optimization

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References

  1. Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: Theory, algorithms and applications. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  2. Borůvka O (1926) O jistém problému minimálnim. Práca Moravské Prirodovědecké Spolnečnosti 3:37–58

    Google Scholar 

  3. Cheriton D, Tarjan RE (1976) Finding minimum spanning trees. SIAM J Comput 5:724–742

    MathSciNet  MATH  Google Scholar 

  4. Cieslik D (1998) Steiner minimal trees. Kluwer, Dordrecht

    MATH  Google Scholar 

  5. Cieslik D (1998) Using Hadwiger numbers in network design. In: DIMACS, 40. Am Math Soc, Providence, pp 59–78

    Google Scholar 

  6. Courant R, Robbins H (1941) What is mathematics? Oxford Univ. Press, Oxford

    Google Scholar 

  7. Dijkstra EW (1959) A note on two problems in connection with graphs. Numer Math 1:269–271

    MathSciNet  MATH  Google Scholar 

  8. Dreyfus SE, Wagner RA (1972) The Steiner problem in graphs. Networks 1:195–207

    MathSciNet  MATH  Google Scholar 

  9. Du D-Z, Hwang FK (1992) A proof of the Gilbert–Pollak conjecture on the Steiner ratio. Algorithmica 7:121–136

    MathSciNet  MATH  Google Scholar 

  10. Fermat P (1934) Abhandlungen über Maxima und Minima. Oswalds Klassiker der exakten Wissenschaft, vol 238. H. Miller, reprint from original.

    Google Scholar 

  11. Ford LR Jr, Fulkerson DR (1956) Maximal flow through a network. Canad J Math 8:399–404

    MathSciNet  MATH  Google Scholar 

  12. Ford LR Jr, Fulkerson DR (1962) Network flow theory. Princeton Univ. Press, Princeton

    Google Scholar 

  13. Foulds LR (1994) Graph theory applications. Springer, Berlin

    Google Scholar 

  14. Garey MR, Johnson DS (1977) The rectilinear Steiner tree problem is NP-complete. SIAM J Appl Math 32:826–834

    MathSciNet  MATH  Google Scholar 

  15. Garey MR, Johnson DS (1979) Computers and intractibility. Freeman, New York

    Google Scholar 

  16. Gauss CF (1917) Briefwechsel Gauss–Schuhmacher. In: Werke, vol. X. pp 459–468

    Google Scholar 

  17. Gavish B (1982) Topological design of centralized computer networks - Formulations and algorithms. Networks 12:355–377

    MathSciNet  MATH  Google Scholar 

  18. Gilbert EN, Pollak HO (1968) Steiner minimal trees. SIAM J Appl Math 16:1–29

    MathSciNet  MATH  Google Scholar 

  19. Graham RL, Hell P (1985) On the history of the minimum spanning tree problem. Ann Hist Comput 7:43–57

    MathSciNet  MATH  Google Scholar 

  20. Grötschel M, Monma CL (1990) Integer polyhedra arising from certain network design problems with connectivity constraints. SIAM J Discret Math 3:502–523

    MATH  Google Scholar 

  21. Grötschel M, Monma CL, Stoer M (1994) Design of survivable networks. In: Handbook Oper Res and Management Sci. North-Holland, Amsterdam

    Google Scholar 

  22. Hakimi SB (1971) Steiner's problem in graphs and its implications. Networks 1:113–133

    MathSciNet  MATH  Google Scholar 

  23. Hakimi SL, Yau SS (1964) Distance matrix of a graph and its realizability. Quart Appl Math 22:305–317

    MathSciNet  Google Scholar 

  24. Horst R, Pardalos PM, Thoai NV (1995) Introduction to global optimization. Kluwer, Dordrecht

    MATH  Google Scholar 

  25. Hwang FK (1976) On Steiner minimal trees with rectilinear distance. SIAM J Appl Math 30:104–114

    MathSciNet  MATH  Google Scholar 

  26. Hwang FK, Richards DS, Winter P (1992) The Steiner tree problem. North-Holland, Amsterdam

    MATH  Google Scholar 

  27. Ivanov AO, Tuzhilin AA (1994) Minimal networks - The Steiner problem and its generalizations. CRC Press, Boca Raton

    MATH  Google Scholar 

  28. Jungnickel D (1994) Graphen, Netzwerke und Algorithmen. BI Wissenschaftsverlag, Mannheim

    Google Scholar 

  29. Karp RM (1962) Reducibility among combinatorial problems. In: Miller RE, Thatcher JW (eds) Complexity of Computer Computations. Springer, New York, pp 85–103

    Google Scholar 

  30. Kruskal JB (1956) On the shortest spanning subtree of a graph and the travelling salesman problem. Proc 7:48–50

    MathSciNet  Google Scholar 

  31. Lawler EL (1976) Combinatorial optimization - Networks and matroids. Holt, Rinehart and Winston, New York

    MATH  Google Scholar 

  32. Lengauer T (1990) Combinatorial algorithms for integrated circuit layout. Teubner and Wiley, Stuttgart

    MATH  Google Scholar 

  33. Love RF, Morris JG (1972) Modelling inter-city road distances by mathematical function. J Oper Res Soc 23:61–71

    MATH  Google Scholar 

  34. Love RF, Morris JG, Wesolowsky G (1989) Facilities location - Models and methods. North-Holland, Amsterdam

    Google Scholar 

  35. Melzak ZA (1961) On the problem of Steiner. Canad Math Bull 4:143–148

    MathSciNet  MATH  Google Scholar 

  36. Papadimitriou CH, Steiglitz K (1982) Combinatorial optimization. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  37. Robins G, Salowe JS (1995) Low-degree minimum spanning trees. Discrete Comput Geom 14:151–165

    MathSciNet  MATH  Google Scholar 

  38. Rubinstein JH, Weng JF (1997) Compression theorems and Steiner ratios on spheres. J Combin Optim 1:67–78

    MathSciNet  MATH  Google Scholar 

  39. Setubal J, Meidanis J (1997) Introduction to computational molecular biology. PWS, Boston, MA

    Google Scholar 

  40. Smith JM (1985) Generalized Steiner network problems in engineering design. In: Design Optimization. pp 119–161

    Google Scholar 

  41. Wald JA, Colbourn CJ (1983) Steiner trees, partial 2-trees, and minimum IFI networks. Networks 13:159–167

    MathSciNet  MATH  Google Scholar 

  42. Winter P (1985) An algorithm for the Steiner problem in the Euclidean plane. Networks 15:323–345

    MathSciNet  MATH  Google Scholar 

  43. Winter P (1986) Generalized Steiner problem in series-parallel networks. J Algorithms 7:549–566

    MathSciNet  MATH  Google Scholar 

  44. Winter P (1987) Steiner problems in networks: A survey. Networks 17:129–167

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University Greifswald, Greifswald, Germany

    Dietmar Cieslik

Authors
  1. Dietmar Cieslik
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Cieslik, D. (2008). Network Design Problems . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_437

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