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Network Design Problems

Part of the Algorithms and Combinatorics 21 book series (AC, volume 21)

Keywords

Span Tree Steiner Tree Vertex Cover Network Design Problem Steiner Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

General Literature

  1. Cheng, X., and Du, D.-Z. [2001]: Steiner Trees in Industry. Kluwer, Dordrecht 2001Google Scholar
  2. Du, D.-Z., Smith, J.M., and Rubinstein, J.H. [2000]: Advances in Steiner Trees. Kluwer, Boston 2000MATHGoogle Scholar
  3. Hwang, F.K., Richards, D.S., and Winter, P. [1992]: The Steiner Tree Problem; Annals of Discrete Mathematics 53. North-Holland, Amsterdam 1992Google Scholar
  4. Goemans, M.X., and 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, 1996Google Scholar
  5. Grötschel, M., Monma, C.L., and 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 1995Google Scholar
  6. Prömel, H.J., and Steger, A. [2002]: The Steiner Tree Problem. Vieweg, Braunschweig 2002MATHGoogle Scholar
  7. Stoer, M. [1992]: Design of Survivable Networks. Springer, Berlin 1992MATHGoogle Scholar
  8. Vazirani, V.V. [2001]: Approximation Algorithms. Springer, Berlin 2001, Chapters 22 and 23Google Scholar

Cited References

  1. Agrawal, A., Klein, P., and Ravi, R. [1995]: When trees collide: an approximation algorithm for the generalized Steiner tree problem in networks. SIAM Journal on Computing 24 (1995), 440–456CrossRefMathSciNetMATHGoogle Scholar
  2. Arora, S. [1998]: Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. Journal of the ACM 45 (1998), 753–782MathSciNetMATHGoogle Scholar
  3. Berman, P., and Ramaiyer, V. [1994]: Improved approximations for the Steiner tree problem. Journal of Algorithms 17 (1994), 381–408CrossRefMathSciNetMATHGoogle Scholar
  4. Bern, M., and Plassmann, P. [1989]: The Steiner problem with edge lengths 1 and 2. Information Processing Letters 32 (1989), 171–176CrossRefMathSciNetMATHGoogle Scholar
  5. Bertsimas, D., and Teo, C. [1995]: From valid inequalities to heuristics: a unified view of primal-dual approximation algorithms in covering problems. Operations Research 46 (1998), 503–514MathSciNetGoogle Scholar
  6. Bertsimas, D., and Teo, C. [1997]: The parsimonious property of cut covering problems and its applications. Operations Research Letters 21 (1997), 123–132CrossRefMathSciNetMATHGoogle Scholar
  7. Borchers, A., and Du, D.-Z. [1997]: The k-Steiner ratio in graphs. SIAM Journal on Computing 26 (1997), 857–869CrossRefMathSciNetMATHGoogle Scholar
  8. Cheriyan, J., and Vetta, A. [2005]: Approximation algorithms for network design with metric costs. Proceedings of the 37th Annual ACM Symposium on Theory of Computing (2005), 167–175Google Scholar
  9. Choukhmane, E. [1978]: Une heuristique pour le problème de l’arbre de Steiner. RAIRO Recherche Opérationnelle 12 (1978), 207–212MathSciNetMATHGoogle Scholar
  10. Clementi, A.E.F., and Trevisan, L. [1999]: Improved non-approximability results for minimum vertex cover with density constraints. Theoretical Computer Science 225 (1999), 113–128CrossRefMathSciNetMATHGoogle Scholar
  11. Dreyfus, S.E., and Wagner, R.A. [1972]: The Steiner problem in graphs. Networks 1 (1972), 195–207MathSciNetMATHGoogle Scholar
  12. Du, D.-Z., and Hwang, F.K. [1992]: A proof of the Gilbert-Pollak conjecture on the Steiner ratio. Algorithmica 7 (1992), 121–135CrossRefMathSciNetMATHGoogle Scholar
  13. Du, D.-Z., Zhang, Y., and Feng, Q. [1991]: On better heuristic for Euclidean Steiner minimum trees. Proceedings of the 32nd Annual Symposium on the Foundations of Computer Science (1991), 431–439Google Scholar
  14. Erickson, R.E., Monma, C.L., and Veinott, A.F., Jr. [1987]: Send-and-split method for minimum concave-cost network flows. Mathematics of Operations Research 12 (1987), 634–664MathSciNetCrossRefMATHGoogle Scholar
  15. Fleischer, L., Jain, K., and Williamson, D.P. [2001]: An iterative rounding 2-approximation algorithm for the element connectivity problem. Proceedings of the 42nd Annual Symposium on the Foundations of Computer Science (2001), 339–347Google Scholar
  16. Gabow, H.N. [2003]: Better performance bounds for finding the smallest k-edge connected spanning subgraph of a multigraph. Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (2003), 460–469Google Scholar
  17. Gabow, H.N., Goemans, M.X., and Williamson, D.P. [1998]: An efficient approximation algorithm for the survivable network design problem. Mathematical Programming B 82 (1998), 13–40MathSciNetGoogle Scholar
  18. Gabow, H.N., Goemans, M.X., Tardos, É., and 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), 562–571Google Scholar
  19. Garey, M.R., Graham, R.L., and Johnson, D.S. [1977]: The complexity of computing Steiner minimal trees. SIAM Journal of Applied Mathematics 32 (1977), 835–859MathSciNetMATHGoogle Scholar
  20. Garey, M.R., and Johnson, D.S. [1977]: The rectilinear Steiner tree problem is NP-complete. SIAM Journal on Applied Mathematics 32 (1977), 826–834MathSciNetMATHGoogle Scholar
  21. Gilbert, E.N., and Pollak, H.O. [1968]: Steiner minimal trees. SIAM Journal on Applied Mathematics 16 (1968), 1–29MathSciNetMATHGoogle Scholar
  22. Goemans, M.X., and Bertsimas, D.J. [1993]: Survivable networks, linear programming and the parsimonious property, Mathematical Programming 60 (1993), 145–166CrossRefMathSciNetGoogle Scholar
  23. Goemans, M.X., Goldberg, A.V., Plotkin, S., Shmoys, D.B., Tardos, É., and Williamson, D.P. [1994]: Improved approximation algorithms for network design problems. Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms (1994), 223–232Google Scholar
  24. Goemans, M.X., and Williamson, D.P. [1995]: A general approximation technique for constrained forest problems. SIAM Journal on Computing 24 (1995), 296–317CrossRefMathSciNetMATHGoogle Scholar
  25. Gröpl, C., Hougardy, S., Nierhoff, T., and Pröomel, H.J. [2001]: Approximation algorithms for the Steiner tree problem in graphs. In: Cheng and Du [2001], pp. 235–279Google Scholar
  26. Hanan, M. [1966]: On Steiner’s problem with rectilinear distance. SIAM Journal on Applied Mathematics 14 (1966), 255–265CrossRefMathSciNetMATHGoogle Scholar
  27. Hetzel, A. [1995]: Verdrahtung im VLSI-Design: Spezielle Teilprobleme und ein sequentielles Lösungsverfahren. Ph.D. thesis, University of Bonn, 1995Google Scholar
  28. Hougardy, S., and 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), 448–453Google Scholar
  29. Hwang, F.K. [1976]: On Steiner minimal trees with rectilinear distance. SIAM Journal on Applied Mathematics 30 (1976), 104–114CrossRefMathSciNetMATHGoogle Scholar
  30. Jain, K. [2001]: A factor 2 approximation algorithm for the generalized Steiner network problem. Combinatorica 21 (2001), 39–60CrossRefMathSciNetMATHGoogle Scholar
  31. Jothi, R., Raghavachari, B., and 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), 725–734Google Scholar
  32. 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. 85–103Google Scholar
  33. Karpinski, M., and Zelikovsky, A. [1997]: New approximation algorithms for Steiner tree problems. Journal of Combinatorial Optimization 1 (1997), 47–65CrossRefMathSciNetMATHGoogle Scholar
  34. Khuller, S., and Raghavachari, B. [1996]: Improved approximation algorithms for uniform connectivity problems. Journal of Algorithms 21 (1996), 434–450CrossRefMathSciNetMATHGoogle Scholar
  35. Khuller, S., and Vishkin, U. [1994]: Biconnectivity augmentations and graph carvings. Journal of the ACM 41 (1994), 214–235CrossRefMathSciNetMATHGoogle Scholar
  36. Klein, P., and Ravi, R. [1993]: When cycles collapse: a general approximation technique for constrained two-connectivity problems. Proceedings of the 3rd MPS Conference on Integer Programming and Combinatorial Optimization (1993), 39–55Google Scholar
  37. Korte, B., Prömel, H.J., and 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. 185–214Google Scholar
  38. Kortsarz, G., Krauthgamer, R., and Lee, J.R. [2002]: Hardness of approximation for vertex-connectivity network design problems. SIAM Journal on Computing 33 (2004), 704–720MathSciNetGoogle Scholar
  39. Kou, L. [1990]: A faster approximation algorithm for the Steiner problem in graphs. Acta Informatica 27 (1990), 369–380CrossRefMathSciNetMATHGoogle Scholar
  40. Kou, L., Markowsky, G., and Berman, L. [1981]: A fast algorithm for Steiner trees. Acta Informatica 15 (1981), 141–145CrossRefMathSciNetMATHGoogle Scholar
  41. Martin, A. [1992]: Packen von Steinerbäumen: Polyedrische Studien und Anwendung. Ph.D. thesis, Technical University of Berlin 1992 [in German]Google Scholar
  42. Mehlhorn, K. [1988]: A faster approximation algorithm for the Steiner problem in graphs. Information Processing Letters 27 (1988), 125–128CrossRefMathSciNetMATHGoogle Scholar
  43. Melkonian, V., and Tardos, É. [2004]: Algorithms for a network design problem with crossing supermodular demands. Networks 43 (2004), 256–265CrossRefMathSciNetMATHGoogle Scholar
  44. Robins, G., and Zelikovsky, A. [2000]: Improved Steiner tree approximation in graphs. Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms (2000), 770–779Google Scholar
  45. Takahashi, M., and Matsuyama, A. [1980]: An approximate solution for the Steiner problem in graphs. Mathematica Japonica 24 (1980), 573–577MathSciNetMATHGoogle Scholar
  46. Thimm, M. [2003]: On the approximability of the Steiner tree problem. Theoretical Computer Science 295 (2003), 387–402CrossRefMathSciNetMATHGoogle Scholar
  47. Warme, D.M., Winter, P., and 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. 81–116Google Scholar
  48. Williamson, D.P., Goemans, M.X., Mihail, M., and Vazirani, V.V. [1995]: A primal-dual approximation algorithm for generalized Steiner network problems. Combinatorica 15 (1995), 435–454CrossRefMathSciNetMATHGoogle Scholar
  49. Zelikovsky, A.Z. [1993]: An 11/6-approximation algorithm for the network Steiner problem. Algorithmica 9 (1993), 463–470CrossRefMathSciNetMATHGoogle Scholar

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