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Network Design with Weighted Degree Constraints

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WALCOM: Algorithms and Computation (WALCOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5431))

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Abstract

In an undirected graph G = (V,E) with a weight function \(w: E \times V \rightarrow \mathbb Q_+\), the weighted degree d w (v;E) of a vertex v is defined as ∑ {w(e,v) |e ∈ E incident with  v}. In this paper, we consider a network design problem which has upper-bounds on weighted degrees of vertices as its constraints while the objective is to compute a minimum cost graph with a prescribed connectivity. We propose bi-criteria approximation algorithms based on the iterative rounding, which has been successfully applied to the degree-bounded network design problem. A problem minimizing the maximum weighted degree of vertices is also discussed.

This work was partially supported by Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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References

  1. Bansal, N., Khandekar, R., Nagarajan, V.: Additive guarantees for degree bounded directed network design. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 769–778 (2008)

    Google Scholar 

  2. Chaudhuri, K., Rao, S., Riesenfeld, S., Talwar, K.: What would Edmonds do? augmenting paths and witnesses for degree-bounded MSTs. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds.) APPROX 2005 and RANDOM 2005. LNCS, vol. 3624, pp. 26–39. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Chaudhuri, K., Rao, S., Riesenfeld, S., Talwar, K.: A push-relabel algorithm for approximating degree bounded MSTs. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 191–201. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  4. Fürer, M., Raghavachari, B.: Approximating the minimum-degree Steiner tree to within one of optimal. Journal of Algorithms 17(3), 409–423 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ghodsi, M., Mahini, H., Mirjalali, K., Gharan, S.O., Sayedi, A.S., Zadimoghaddam, R.M.: Spanning trees with minimum weighted degrees. Information Processing Letters 104, 113–116 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. 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 

  7. Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer, Heidelberg (1988)

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Kiraly, 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)

    Chapter  Google Scholar 

  10. Könemann, J., Ravi, R.: A matter of degree: Improved approximation algorithms for degree-bounded minimum spanning trees. SIAM Journal on Computing 31(6), 1783–1793 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Könemann, J., Ravi, R.: Primal-dual meets local search: approximating MST’s with nonuniform degree bounds. SIAM Journal on Computing 34, 763–773 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lau, L.C., Naor, J.S., Singh, M., Salavatipour, M.R.: Survivable network design with degree or order constraints. In: Proceedings of the 39th ACM Symposium on Theory of Computing (STOC), pp. 651–660 (2007)

    Google Scholar 

  13. Lau, L.C., Singh, M.: Additive approximation for bounded degree survivable network design. In: Proceedings of the 40th ACM Symposium on Theory of Computing (STOC), pp. 759–768 (2008)

    Google Scholar 

  14. Nutov, Z.: Approximating directed weighted-degree constrained networks. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 219–232. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Ravi, R.: Steiner Trees and Beyond: Approximation Algorithms for Network Design. PhD thesis, Department of Computer Science, Brown University (1993)

    Google Scholar 

  16. Ravi, R., Marathe, M.V., Ravi, S.S., Rosenkrantz, D.J., Hunt III, H.B.: Many birds with one stone: Multi-objective approximation algorithms. In: Proceedings of the 25th ACM Symposium on Theory of Computing, pp. 438–447 (1993)

    Google Scholar 

  17. Ravi, R., Singh, M.: Delegate and conquer: An LP-based approximation algorithm for minimum degree MSTs. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 169–180. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. 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 

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Authors and Affiliations

  1. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan

    Takuro Fukunaga & Hiroshi Nagamochi

Authors
  1. Takuro Fukunaga
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  2. Hiroshi Nagamochi
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Editors and Affiliations

  1. Indian Statistical Institute, 700 108, Kolkata, India

    Sandip Das

  2. Japan Advanced Institute of Science and Technology, 923-1292, Ishikawa, Japan

    Ryuhei Uehara

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Fukunaga, T., Nagamochi, H. (2009). Network Design with Weighted Degree Constraints. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_19

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  • DOI: https://doi.org/10.1007/978-3-642-00202-1_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00201-4

  • Online ISBN: 978-3-642-00202-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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