Document Open Access Logo

Approximating the Generalized Terminal Backup Problem via Half-integral Multiflow Relaxation

Author Takuro Fukunaga

PDF

File

Thumbnail PDF
PDF
LIPIcs.STACS.2015.316.pdf
  • Filesize: 0.61 MB
  • 13 pages

Document Identifiers

Subject Classification

Keywords
  • survivable network design
  • multiflow
  • LP rounding

Metrics

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

Abstract

We consider a network design problem called the generalized terminal backup problem. Whereas earlier work investigated the edge-connectivity constraints only, we consider both edge- and node-connectivity constraints for this problem. A major contribution of this paper is 
the development of a strongly polynomial-time 4/3-approximation algorithm for the problem. Specifically, we show that a linear programming relaxation of the problem is half-integral, and that the half-integral optimal solution can be rounded to a 4/3-approximate solution. We also prove that the linear programming relaxation of the problem with the edge-connectivity constraints is equivalent to minimizing the cost of half-integral multiflows that satisfy flow demands given from terminals. This observation implies a strongly polynomial-time algorithm for computing a minimum cost half-integral multiflow under flow demand constraints.

Cite As Get BibTex

Takuro Fukunaga. Approximating the Generalized Terminal Backup Problem via Half-integral Multiflow Relaxation. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 316-328, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.STACS.2015.316

Author Details

Takuro Fukunaga

References

  1. Elliot Anshelevich and Adriana Karagiozova. Terminal backup, 3D matching, and covering cubic graphs. SIAM Journal on Computing, 40(3):678-708, 2011. Google Scholar
  2. Maxim A. Babenko and Alexander V. Karzanov. Min-cost multiflows in node-capacitated undirected networks. Journal of Combinatorial Optimization, 24(3):202-228, 2012. Google Scholar
  3. Attila Bernáth and Yusuke Kobayashi. The generalized terminal backup problem. In SODA, pages 1678-1686, 2014. Google Scholar
  4. Michel Burlet and Alexander V. Karzanov. Minimum weight (T, d)-joins and multi-joins. Discrete Mathematics, 181(1-3):65-76, 1998. Google Scholar
  5. Boris V. Cherkassky. A solution of a problem on multicommodity flows in a network. Ekonomika i Matematicheskie Metody, 13(1):143-151, 1977. Google Scholar
  6. Lisa Fleischer, Kamal Jain, and David 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
  7. Hiroshi Hirai. Half-integrality of node-capacitated multiflows and tree-shaped facility locations on trees. Mathematical Programming, 137(1-2):503-530, 2013. Google Scholar
  8. Hiroshi Hirai. L-extendable functions and a proximity scaling algorithm for minimum cost multiflow problem. ArXiv e-prints, November 2014. Google Scholar
  9. Kamal Jain. A factor 2 approximation algorithm for the generalized Steiner network problem. Combinatorica, 21(1):39-60, 2001. Google Scholar
  10. Alexander V. Karzanov. A problem on maximum multifow of minimum cost. Combinatorial Methods for Flow Problems, pages 138-156, 1979. in Russian. Google Scholar
  11. Alexander V. Karzanov. Minimum cost multifows in undirected networks. Mathematical Programming, 66(3):313-325, 1994. Google Scholar
  12. László Lovász. On some connectivity properties of Eulerian graphs. Acta Mathematica Hungarica, 28(1):129-138, 1976. Google Scholar
  13. Alexander Schrijver. Combinatorial Optimization - Polyhedra and Efficiency. Springer, 2003. Google Scholar
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

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