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A Unified Algorithm for Degree Bounded Survivable Network Design

  • Lap Chi Lau
  • Hong Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8494)

Abstract

We present an approximation algorithm for the minimum bounded degree Steiner network problem that returns a Steiner network of cost at most two times the optimal and the degree on each vertex v is at most min {b v  + 3r max , 2b v  + 2}, where r max is the maximum connectivity requirement and b v is the given degree bound on v. This unifies, simplifies, and improves the previous results for this problem.

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References

  1. 1.
    Bansal, N., Khandekar, R., Nagarajan, V.: Additive guarantees for degree bounded directed network design. SIAM Journal on Computing 29, 1413–1431 (2009)MathSciNetGoogle Scholar
  2. 2.
    Cheriyan, J., Vegh, L.: Approximating minimum-cost k-node connected subgraphs via independence-free graphs. In: Proceedings of the 54th Annual IEEE Symposium on Foundations of Computer Science (FOCS) (2013)Google Scholar
  3. 3.
    Cheriyan, J., Vempala, S., Vetta, A.: Network design via iterative rounding of setpair relaxations. Combinatorica 26(3), 255–275 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Fleischer, L., Jain, K., Williamson, D.P.: Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems. J. Comput. Syst. Sci. 72(5), 838–867 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Fukunaga, T., Ravi, R.: Iterative rounding approximation algorithms for degree-bounded node-connectivity network design. In: Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 263–272 (2012)Google Scholar
  6. 6.
    Fürer, M., Raghavachari, B.: Approximating the minimum-degree Steiner tree to within one of optimal. J. of Algorithms 17(3), 409–423 (1994)CrossRefGoogle Scholar
  7. 7.
    Gabow, H.N.: On the L  ∞ -norm of extreme points for crossing supermodular directed network LPs. In: Jünger, M., Kaibel, V. (eds.) IPCO 2005. LNCS, vol. 3509, pp. 392–406. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Goemans, M.X.: Minimum Bounded-Degree Spanning Trees. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, pp. 273–282 (2006)Google Scholar
  9. 9.
    Jain, K.: A factor 2-approximation algorithm for the generalized steiner network problem. Combinatorica 21(1), 39–60 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Khandekar, R., Kortsarz, G., Nutov, Z.: On some network design problems with degree constraints. Journal of Computer and System Sciences 79(5), 725–736 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Király, T., Lau, L.C., Singh, M.: Degree Bounded Matroids and Submodular Flows. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds.) IPCO 2008. LNCS, vol. 5035, pp. 259–272. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Lau, L.C., Naor, S., Salavatipour, M., Singh, M.: Survivable network design with degree or order constraints. SIAM Journal on Computing 39(3), 1062–1087 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Lau, L.C., Ravi, R., Singh, M.: Iterative Methods in Combinatorial Optimization. Cambridge University Press (2011)Google Scholar
  14. 14.
    Lau, L.C., Singh, M.: Additive approximation for bounded degree survivable network design. SIAM Journal on Computing 42(6), 2217–2242 (2014)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Louis, A., Vishnoi, N.K.: Improved algorithm for degree bounded survivable network design problem. In: Proceedings of the 12th Scandinavian Symposium and Workshops on Algorithm Theory, pp. 408–419 (2010)Google Scholar
  16. 16.
    Nutov, Z.: Degree-constrained node-connectivity. In: Proceedings of the 10th Latin American Symposium on Theoretical Informatics (LATIN), pp. 582–593 (2012)Google Scholar
  17. 17.
    Singh, M., Lau, L.C.: Approximating minimum bounded degree spanning trees to within one of optimal. In: Proceedings of the 39th ACM Symposium on Theory of Computing (STOC), pp. 661–670 (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lap Chi Lau
    • 1
  • Hong Zhou
    • 1
  1. 1.Department of Computer Science and EngineeringThe Chinese University of Hong KongHong Kong

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