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Approximating Directed Buy-at-Bulk Network Design

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Approximation and Online Algorithms (WAOA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6534))

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Abstract

Buy-at-bulk network design is a well-known problem that has been researched extensively on undirected graphs. In this paper, we initiate the theoretical study of the same problem on directed graphs, thus capturing real-life situations where the cost of installing capacity on an edge is asymmetric with respect to direction, as e.g. in the design of wireless and satellite communication networks.

More specifically, we develop two approximation algorithms for directed buy-at-bulk network design in the non-uniform cost model. Combined, they achieve a ratio of \(O \big( \! \min \big\{ k^{1 / 2 + \epsilon}, n^{4 / 5 + \epsilon} \big\} \big)\) for any constant ε> 0, where n is the number of nodes of the network and k is the number of demand pairs to be connected. Further, the above ratio is independent of the amount of traffic flow requested by each demand pair, which may vary arbitrarily, and it can be remarkably improved when all demand pairs share a common sink (or a common source, symmetrically).

To the best of our knowledge, this is the first non-trivial approximation factor established for the aforementioned problem, and naturally it also applies to more restricted cost models, such as the uniform and rent-or-buy models. Moreover, it essentially matches the best currently known approximation guarantees for directed Steiner forest, which may be viewed as a special case of directed buy-at-bulk network design.

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References

  1. Andrews, M.: Hardness of buy-at-bulk network design. In: Proceedings of IEEE FOCS, pp. 115–124 (2004)

    Google Scholar 

  2. Andrews, M., Zhang, L.: Approximation algorithms for access network design. Algorithmica 34(2), 197–215 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Awerbuch, B., Azar, Y.: Buy-at-bulk network design. In: Proceedings of IEEE FOCS, pp. 542–547 (1997)

    Google Scholar 

  4. Bartal, Y.: Probabilistic approximation of metric spaces and its algorithmic applications. In: Proceedings of IEEE FOCS, pp. 184–193 (1996)

    Google Scholar 

  5. Charikar, M., Chekuri, C., Cheung, T., Dai, Z., Goel, A., Guha, S., Li, M.: Approximation algorithms for directed Steiner problems. Journal of Algorithms 33, 73–91 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  6. Charikar, M., Chekuri, C., Goel, A., Guha, S.: Rounding via trees: Deterministic approximation algorithms for group Steiner trees and k-median. In: Proceedings of ACM STOC, pp. 114–123 (1998)

    Google Scholar 

  7. Charikar, M., Karagiozova, A.: On non-uniform multicommodity buy-at-bulk network design. In: Proceedings of ACM STOC, pp. 176–182 (2005)

    Google Scholar 

  8. Chekuri, C., Even, G., Gupta, A., Segev, D.: Set connectivity problems in undirected graphs and the directed Steiner network problem. In: Proceedings of ACM-SIAM SODA, pp. 532–541 (2008)

    Google Scholar 

  9. Chekuri, C., Hajiaghayi, M.T., Kortsarz, G., Salavatipour, M.R.: Approximation algorithms for nonuniform buy-at-bulk network design. SIAM Journal on Computing 39(5), 1772–1798 (2010), http://link.aip.org/link/?SMJ/39/1772/1

    Article  MathSciNet  MATH  Google Scholar 

  10. Chekuri, C., Khanna, S., Naor, J.: A deterministic algorithm for the cost-distance problem. In: Proceedings of ACM-SIAM SODA, pp. 232–233 (2001)

    Google Scholar 

  11. Dodis, Y., Khanna, S.: Designing networks with bounded pairwise distance. In: Proceedings of ACM STOC, pp. 750–759 (1999)

    Google Scholar 

  12. Fakcharoenphol, J., Rao, S., Talwar, K.: A tight bound on approximating arbitrary metrics by tree metrics. Journal of Computer and System Sciences 69, 485–497 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Feldman, M., Kortsarz, G., Nutov, Z.: Improved approximation for the directed Steiner forest problem. In: Proceedings of ACM-SIAM SODA, pp. 922–931 (2009)

    Google Scholar 

  14. Garg, N., Konjevod, G., Ravi, R.: A polylogarithmic approximation algorithm for the group Steiner tree problem. Journal of Algorithms 37, 66–84 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ge, F., Tan, L., Zukerman, M.: Throughput of FAST TCP in asymmetric networks. IEEE Communications Letters 12(2), 158–160 (2008)

    Article  Google Scholar 

  16. Guha, S., Meyerson, A., Munagala, K.: A constant factor approximation for the single sink edge installation problem. SIAM Journal on Computing 38(6), 2426–2442 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Helvig, C.S., Robins, G., Zelikovsky, A.: Improved approximation scheme for the group Steiner problem. Networks 37(1), 8–20 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Meyerson, A.: Online algorithms for network design. In: Proceedings of ACM SPAA, pp. 275–280 (2004)

    Google Scholar 

  19. Meyerson, A., Munagala, K., Plotkin, S.: Cost-distance: Two metric network design. SIAM Journal on Computing 38(4), 1648–1659 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Obata, H., Ishida, K., Funasaka, J., Amano, K.: TCP performance analysis on asymmetric networks composed of satellite and terrestrial links. In: Proceedings of IEEE ICNP, pp. 199–206 (2000)

    Google Scholar 

  21. Ramanathan, S.: Multicast tree generation in networks with asymmetric links. IEEE/ACM Transactions on Networking 4(4), 558–568 (1996)

    Article  Google Scholar 

  22. Ramasubramanian, V., Mossé, D.: BRA: A bidirectional routing abstraction for asymmetric mobile ad hoc networks. IEEE/ACM Transactions on Networking 16(1), 116–129 (2008)

    Article  Google Scholar 

  23. Salman, F.S., Cheriyan, J., Ravi, R., Subramanian, S.: Buy at bulk network design: Approximating the single-sink edge installation problem. SIAM Journal on Optimization 11(3), 595–610 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  24. Zelikovsky, A.: A series of approximation algorithms for the acyclic directed Steiner tree problem. Algorithmica 18, 99–110 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Bell Laboratories, Alcatel-Lucent, 600-700 Mountain Avenue, Murray Hill, NJ, 07974, USA

    Spyridon Antonakopoulos

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  1. Spyridon Antonakopoulos
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Editors and Affiliations

  1. Department of Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  2. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Roberto Solis-Oba

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Antonakopoulos, S. (2011). Approximating Directed Buy-at-Bulk Network Design. In: Jansen, K., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2010. Lecture Notes in Computer Science, vol 6534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18318-8_2

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  • DOI: https://doi.org/10.1007/978-3-642-18318-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18317-1

  • Online ISBN: 978-3-642-18318-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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