Document Open Access Logo

Single-Sink Fractionally Subadditive Network Design

Authors Guru Guruganesh, Jennifer Iglesias, R. Ravi, Laura Sanita

PDF

File

Thumbnail PDF
PDF
LIPIcs.ESA.2017.46.pdf
  • Filesize: 0.51 MB
  • 13 pages

Document Identifiers

Subject Classification

Keywords
  • Network design
  • single-commodity flow
  • approximation algorithms
  • Steiner tree

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

We study a generalization of the Steiner tree problem, where we are given a weighted network G together with a collection of k subsets of its vertices and a root r. We wish to construct a minimum cost network such that the network supports one unit of flow to the root from every node in a subset simultaneously. The network constructed does not need to support flows from all the subsets simultaneously.

We settle an open question regarding the complexity of this problem for k=2, and give a 3/2-approximation algorithm that improves over a (trivial) known 2-approximation. Furthermore, we prove some structural results that prevent many well-known techniques from doing better than the known O(log n)-approximation. Despite these obstacles, we conjecture that this problem should have an O(1)-approximation. We also give an approximation result for a variant of the problem where the solution is required to be a path.

Cite As Get BibTex

Guru Guruganesh, Jennifer Iglesias, R. Ravi, and Laura Sanita. Single-Sink Fractionally Subadditive Network Design. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 46:1-46:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ESA.2017.46

Author Details

Guru Guruganesh
Jennifer Iglesias
R. Ravi
Laura Sanita

References

  1. M. Balcan, F. Constantin, S. Iwata, and L. Wang. Learning valuation functions. In Conference on Learning Theory, volume 23, pages 4-1, 2012. Google Scholar
  2. W. Ben-Ameur and H. Kerivin. Routing of uncertain demands. Optimization and Engineering, 3:283-313, 2005. Google Scholar
  3. K. Bhawalkar and T. Roughgarden. Welfare guarantees for combinatorial auctions with item bidding. In Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms, pages 700-709. Society for Industrial and Applied Mathematics, 2011. Google Scholar
  4. D. Chakrabarty and C. Swamy. Facility location with client latencies: LP-based techniques for minimum-latency problems. Mathematics of Operations Research, 41(3):865-883, 2016. Google Scholar
  5. C. Chekuri. Routing and network design with robustness to changing or uncertain traffic demands. SIGACT News, 38(3):106-128, 2007. Google Scholar
  6. M. Chlebik and J. Chlebikova. Approximation hardness of the steiner tree problem on graphs. Proc. of the Scandinavian Workshop on Algorithm Theory, pages 170-179, 2002. Google Scholar
  7. N. G. Duffield, P. Goyal, A. G. Greenberg, P. P. Mishra, K. K. Ramakrishnan, and J. E. van der Merwe. A flexible model for resource management in virtual private networks. Proceedings of SIGCOMM, 29:95-108, 1999. Google Scholar
  8. J. Fakcharoenphol, S. Rao, and K. Talwar. A tight bound on approximating arbitrary metrics by tree metrics. Journal of Computer and System Sciences, 69:485-497, 2004. Google Scholar
  9. U. Feige. On maximizing welfare when utility functions are subadditive. SIAM Journal on Computing, 39(1):122-142, 2009. Google Scholar
  10. A. E. Feldmann, J. Könemann, K. Pashkovich, and L. Sanità. Fast approximation algorithms for the generalized survivable network design problem. Proceedings of ISAAC (International symposium on algorithms and computation), pages 33:1- 33:12, 2016. Google Scholar
  11. J. Fingerhut, S. Suri, and J. Turner. Designing least-cost nonblocking broadband networks. Journal of Algorithms, 24(2):287-309, 1997. Google Scholar
  12. M. X. Goemans and D. P. Williamson. A general approximation technique for constrained forest problems. SIAM Journal on Computing, 24(2):296-317, 1995. Google Scholar
  13. N. Goyal, N. Olver, and F. B. Shepherd. Dynamic vs. oblivious routing in network design. Algorithmica, 61(1):161-173, 2011. Google Scholar
  14. N. Goyal, N. Olver, and F. B. Shepherd. The VPN conjecture is true. Journal of the ACM, 60(3):17:1-17:17, June 2013. Google Scholar
  15. F. Grandoni, T. Rothvoß, and L. Sanità. From uncertainty to non-linearity: Solving virtual private network via single-sink buy-at-bulk. Mathematics of Operations Research, 36(2):185-204, 2011. Google Scholar
  16. A. Gupta, J. Kleingerg, R. Kumar, B. Rastogi, and B. Yener. Provisioning a virtual private network: A network design problem for multicommodity flow. Proceedings of Symposium on Theory of Computing (STOC), pages 389-398, 2001. Google Scholar
  17. A. Gupta, V. Nagarajan, and R. Ravi. An improved approximation algorithm for requirement cut. Operations Research Letters, 38(4):322-325, 2010. Google Scholar
  18. G. Guruganesh, J. Iglesias, R. Ravi, and L. Sanità. Plane gossip: Approximating rumor spread in planar graphs. arXiv preprint arXiv:1707.01487, 2017. Google Scholar
  19. K. Jain. A factor 2 approximation algorithm for the generalized steiner network problem. Combinatorica, 21(1):39-60, 2001. Google Scholar
  20. B. Lehmann, D. Lehmann, and N. Nisan. Combinatorial auctions with decreasing marginal utilities. In Proc. of the 3rd ACM Conf. on Electronic Commerce, pages 18-28. ACM, 2001. Google Scholar
  21. G. Oriolo, L. Sanità, and R. Zenklusen. Network design with a discrete set of traffic matrices. Operations Research Letters, 41(4):390-396, 2013. Google Scholar
  22. M. Yannakakis. Node-and edge-deletion np-complete problems. In Proceedings of the tenth annual ACM symposium on Theory of computing, pages 253-264. ACM, 1978. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact