Document Open Access Logo

A Note on Iterated Rounding for the Survivable Network Design Problem

Authors Chandra Chekuri, Thapanapong Rukkanchanunt

PDF
Thumbnail PDF

File

OASIcs.SOSA.2018.2.pdf
  • Filesize: 0.5 MB
  • 10 pages

Document Identifiers

Author Details

Chandra Chekuri
Thapanapong Rukkanchanunt

Cite AsGet BibTex

Chandra Chekuri and Thapanapong Rukkanchanunt. A Note on Iterated Rounding for the Survivable Network Design Problem. In 1st Symposium on Simplicity in Algorithms (SOSA 2018). Open Access Series in Informatics (OASIcs), Volume 61, pp. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/OASIcs.SOSA.2018.2

Abstract

In this note we consider the survivable network design problem (SNDP) in undirected graphs. We make two contributions. The first is a new counting argument in the iterated rounding based 2-approximation for edge-connectivity SNDP (EC-SNDP) originally due to Jain. The second contribution is to make some connections between hypergraphic version of SNDP (Hypergraph-SNDP) introduced by Zhao, Nagamochi and Ibaraki, and edge and node-weighted versions of EC-SNDP and element-connectivity SNDP (Elem-SNDP). One useful consequence is a 2-approximation for Elem-SNDP that avoids the use of set-pair based relaxation and analysis.
Keywords
  • survivable network design
  • iterated rounding
  • approximation
  • element connectivity

Metrics

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

References

  1. Nikhil Bansal, Rohit Khandekar, and Viswanath Nagarajan. Additive guarantees for degree-bounded directed network design. SIAM Journal on Computing, 39(4):1413-1431, 2009. Google Scholar
  2. Tanmoy Chakraborty, Julia Chuzhoy, and Sanjeev Khanna. Network design for vertex connectivity. In Proceedings of the fortieth annual ACM symposium on Theory of computing, pages 167-176. ACM, 2008. Google Scholar
  3. Chandra Chekuri, Alina Ene, and Ali Vakilian. Node-weighted network design in planar and minor-closed families of graphs. In Automata, Languages, and Programming, pages 206-217. Springer, 2012. Google Scholar
  4. Chandra Chekuri, Alina Ene, and Ali Vakilian. Prize-collecting survivable network design in node-weighted graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, pages 98-109. Springer, 2012. Google Scholar
  5. J. Cheriyan, S. Vempala, and A. Vetta. Network design via iterative rounding of setpair relaxations. Combinatorica, 26(3):255-275, 2006. Google Scholar
  6. Julia Chuzhoy and Sanjeev Khanna. An O(k³ log n)-approximation algorithm for vertex-connectivity survivable network design. Theory of Computing, 8:401-413, 2012. Preliminary version in Proc. of IEEE FOCS, 2009. Google Scholar
  7. L. Fleischer, K. Jain, and D.P. Williamson. Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems. Journal of Computer and System Sciences, 72(5):838-867, 2006. Google Scholar
  8. Takuro Fukunaga. Spider covers for prize-collecting network activation problem. In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '15, pages 9-24. SIAM, 2015. URL: http://dl.acm.org/citation.cfm?id=2722129.2722131.
  9. M.X. Goemans, A.V. Goldberg, S. Plotkin, D.B. Shmoys, E. Tardos, and D.P. Williamson. Improved approximation algorithms for network design problems. In Proc. of ACM-SIAM SODA, pages 223-232, 1994. Google Scholar
  10. K. Jain. A factor 2 approximation algorithm for the generalized Steiner network problem. Combinatorica, 21(1):39-60, 2001. Preliminary version in FOCS 1998. Google Scholar
  11. P. Klein and R. Ravi. A nearly best-possible approximation algorithm for node-weighted Steiner trees. J. Algorithms, 19(1):104-115, 1995. Preliminary version in IPCO 1993. Google Scholar
  12. Lap Chi Lau, Ramamoorthi Ravi, and Mohit Singh. Iterative methods in combinatorial optimization, volume 46. Cambridge University Press, 2011. Google Scholar
  13. Viswanath Nagarajan, R Ravi, and Mohit Singh. Simpler analysis of lp extreme points for traveling salesman and survivable network design problems. Operations Research Letters, 38(3):156-160, 2010. Google Scholar
  14. Z. Nutov. Approximating minimum cost connectivity problems via uncrossable bifamilies and spider-cover decompositions. In Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 417-426. IEEE, 2009. Google Scholar
  15. David P Williamson and David B Shmoys. The design of approximation algorithms. Cambridge university press, 2011. Google Scholar
  16. Liang Zhao, Hiroshi Nagamochi, and Toshihide Ibaraki. A note on approximating the survivable network design problem in hypergraphs. IEICE TRANSACTIONS on Information and Systems, 85(2):322-326, 2002. Google Scholar
  17. Liang Zhao, Hiroshi Nagamochi, and Toshihide Ibaraki. A primal-dual approximation algorithm for the survivable network design problem in hypergraphs. Discrete applied mathematics, 126(2):275-289, 2003. Preliminary version appeared in Proc. of STACS, 2001. Google Scholar
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact