Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Approximating Minimum-Power k-Connectivity

  • Conference paper
Ad-hoc, Mobile and Wireless Networks (ADHOC-NOW 2008)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 5198))

Included in the following conference series:

  • 641 Accesses

Abstract

The Minimum-Power k -Connected Subgraph (MP k CS) problem seeks a power (range) assignment to the nodes of a given wireless network such that the resulting communication (sub)network is k-connected and the total power is minimum. We give a new very simple approximation algorithm for this problem that significantly improves the previously best known approximation ratios. Specifically, the approximation ratios of our algorithm are:

  • 3 (improving (3 + 2/3)) for k = 2,

  • 4 (improving (5 + 2/3)) for k = 3,

  • k + 3 for k ∈ {4,5} and k + 5 for k ∈ {6,7} (improving k + 2⌈(k + 1)/2⌉),

  • 3(k − 1) (improving 3k) for any constant k.

Our results are based on a (k + 1)-approximation algorithm (improving the ratio k + 4) for the problem of finding a Min-Power k -Inconnected Subgraph, which is of independent interest.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Althaus, E., Calinescu, G., Mandoiu, I., Prasad, S., Tchervenski, N., Zelikovsky, A.: Power efficient range assignment for symmetric connectivity in static ad-hoc wireless networks. Wireless Networks 12(3), 287–299 (2006)

    Article  Google Scholar 

  2. Auletta, V., Dinitz, Y., Nutov, Z., Parente, D.: A 2-approximation algorithm for finding an optimum 3-vertex-connected spanning subgraph. J. of Algorithms 32(1), 21–30 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Calinescu, G., Kapoor, S., Olshevsky, A., Zelikovsky, A.: Network lifetime and power assignment in ad hoc wireless networks. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 114–126. Springer, Heidelberg (2003)

    Google Scholar 

  4. Calinescu, G., Wan, P.J.: Range assignment for biconnectivity and k-edge connectivity in wireless ad hoc networks. Mobile Networks and Applications 11(2), 121–128 (2006)

    Article  Google Scholar 

  5. Cheriyan, J., Vempala, S., Vetta, A.: An approximation algorithm for the minimum-cost k-vertex connected subgraph. SIAM J. on Computing 32(4), 1050–1055 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dinitz, Y., Nutov, Z.: A 3-approximation algorithm for finding optimum 4,5-vertex-connected spanning subgraphs. J. of Algorithms 32(1), 31–40 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Fackharoenphol, J., Laekhanukit, B.: An O(log2 k)-approximation algorithm for the k-vertex connected spanning subgraph problem. In: STOC, pp. 153–158 (2008)

    Google Scholar 

  8. Frank, A., Tardos, E.: An application of submodular flows. Linear Algebra and its Applications 114/115, 329–348 (1989)

    Article  MathSciNet  Google Scholar 

  9. Hajiaghayi, M.T., Kortsarz, G., Mirrokni, V.S., Nutov, Z.: Power optimization for connectivity problems. Math. Program. 110(1), 195–208 (2007); Preliminary version in IPCO 2005

    Article  MATH  MathSciNet  Google Scholar 

  10. Halin, R.: A theorem on n-connected graphs. J. Combinatorial Theory 7, 150–154 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  11. Jia, X., Kim, D., Makki, S., Wan, P.J., Yi, C.W.: Power assignment for k-connectivity in wireless ad hoc networks. J. Comb. Optim. 9(2), 213–222 (2005); Preliminary version in INFOCOM 2005

    Article  MATH  MathSciNet  Google Scholar 

  12. Kortsarz, G., Mirrokni, V.S., Nutov, Z., Tsanko, E.: Approximating minimum-power degree and connectivity problems. In: LATIN, pp. 423–435 (2008)

    Google Scholar 

  13. Kortsarz, G., Nutov, Z.: Approximating minimum-power edge-covers and 2,3-connectivity. Manuscript (submitted for journal publication)

    Google Scholar 

  14. Kortsarz, G., Nutov, Z.: Approximating node-connectivity problems via set covers. Algorithmica 37, 75–92 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kortsarz, G., Nutov, Z.: Approximating k-node connected subgraphs via critical graphs. SIAM J. on Computing 35(1), 247–257 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kortsarz, G., Nutov, Z.: Approximating minimum-cost connectivity problems. In: Gonzalez, T.F. (ed.) Approximation algorithms and Metaheuristics, ch. 58. Chapman & Hall/CRC, Boca Raton (2007)

    Google Scholar 

  17. Lando, Y., Nutov, Z.: On minimum power connectivity problems. Preliminary version in ESA 2007, pp. 87–98 (manuscript, submitted for journal publication)

    Google Scholar 

  18. Lando, Y., Nutov, Z.: Inapproximability of survivable networks. In: APPROX (to appear 2008)

    Google Scholar 

  19. Mader, W.: Ecken vom grad n in minimalen n-fach zusammenhängenden graphen. Archive der Mathematik 23, 219–224 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  20. Nutov, Z.: An almost O(logk)-approximation for k-connected subgraphs (manuscript)

    Google Scholar 

  21. Nutov, Z.: Approximating minimum power covers of intersecting families and directed connectivity problems. In: Díaz, J., Jansen, K., Rolim, J., Zwick, U. (eds.) APPROX 2006. LNCS, vol. 4110, pp. 236–247. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Schrijver, A.: Combinatorial Optimization, Polyhedra and Efficiency. Springer, Berlin (2004)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Open University of Israel, Raanana, Israel

    Zeev Nutov

Authors
  1. Zeev Nutov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Centre de Recherche, INRIA Sophia Antipolis, Mascotte, INRIA, I3S, CNRS UMR 6070, Univ. Nice Sophia, 06902, Sophia-Antipolis Cedex, France

    David Coudert

  2. Centre de recherche INRIA Lille, IRCICA/LIFL, CNRS UMR 8022, Univ. Lille, BP 70478, 59658, Villeneuve d’ Ascq, France

    David Simplot-Ryl

  3. SITE, University of Ottawa, K1N 6N5, Ontario, Canada

    Ivan Stojmenovic

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nutov, Z. (2008). Approximating Minimum-Power k-Connectivity. In: Coudert, D., Simplot-Ryl, D., Stojmenovic, I. (eds) Ad-hoc, Mobile and Wireless Networks. ADHOC-NOW 2008. Lecture Notes in Computer Science, vol 5198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85209-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85209-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85208-7

  • Online ISBN: 978-3-540-85209-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation