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Approximating k-outconnected subgraph problems

  • Joseph Cheriyan
  • Tibor Jordán
  • Zeev Nutov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1444)

Abstract

We present approximation algorithms and structural results for problems in network design. We give improved approximation algorithms for finding min-cost k-outconnected graphs with either a single root or multiple roots for (i) uniform costs, and (ii) metric costs. The improvements are obtained by focusing on single-root k-outconnected graphs and proving (i) a version of Mader's critical cycle theorem and (ii) an extension of a splitting off theorem by Bienstock et al.

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References

  1. 1.
    D. Bienstock, E. F. Brickell and C. L. Monma, “On the structure of minimum-weight k-connected spanning networks,” SIAM J. Discrete Math. 3 (1990), 320–329.MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    B. Bollobás, Extremal Graph Theory, Academic Press, London, 1978.Google Scholar
  3. 3.
    J.Cheriyan and R.Thurimella, “Approximating minimum-size k-connected spanning subgraphs via matching,” manuscript, Sept. 1996. ECCC TR98-025, see http://www.eccc.uni-trier.de/eccc-local/Lists/TR-1998.html. Preliminary version in Proc. 37th IEEE FOCS (1996), 292–301.Google Scholar
  4. 4.
    A.Frank and E. Tardos, “An application of submodular flows,” Linear Algebra and its Applications, 114/115 (1989), 320–348.MathSciNetCrossRefGoogle Scholar
  5. 5.
    G.L.Frederickson and J. Ja'Ja', “On the relationship between the biconnectivity augmentation and traveling salesman problems,” Theor. Comp. Sci. 19 (1982), 189–201.MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    H. N. Gabow and R. E. Tarjan, “Faster scaling algorithms for general graph matching problems,” Journal of the ACM 38 (1991), 815–853.MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    T. Jordán, “On the optimal vertex-connectivity augmentation,” J. Combinatorial Theory, Series B 63 (1995), 8–20.MATHCrossRefGoogle Scholar
  8. 8.
    S. Khuller, “Approximation algorithms for finding highly connected subgraphs,” in Approximation algorithms for NP-hard problems, Ed. D. S. Hochbaum, PWS publishing co., Boston, 1996.Google Scholar
  9. 9.
    S. Khuller and B. Raghavachari, “Improved approximation algorithms for uniform connectivity problems,” Journal of Algorithms 21 (1996), 434–450.MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    W. Mader, “Ecken vom Grad n in minimalen n-fach zusammenhÄngenden Graphen,” Archive der Mathematik 23 (1972), 219–224.MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    H.Nagamochi and T.Ibaraki, “A linear-time algorithm for finding a sparse k-connected spanning subgraph of a k-connected graph,” Algorithmica 7 (1992), 583–596.MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Z.Nutov, M.Penn and D.Sinreich, “On mobile robots flow in locally uniform networks,” Canadian Journal of Information Systems and Operational Research 35 (1997), 197–208.Google Scholar
  13. 13.
    R. Ravi and D. P. Williamson, “An approximation algorithm for minimum-cost vertex-connectivity problems.” Algorithmica (1997) 18: 21–43.MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Joseph Cheriyan
    • 1
  • Tibor Jordán
    • 2
  • Zeev Nutov
    • 1
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Institut for Matematik og DatalogiOdense UniversitetOdenseDenmark

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