Convergence Time of Power-Control Dynamics

  • Johannes Dams
  • Martin Hoefer
  • Thomas Kesselheim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)

Abstract

We study two (classes of) distributed algorithms for power control in a general model of wireless networks. There are n wireless communication requests or links that experience interference and noise. To be successful a link must satisfy an SINR constraint. The goal is to find a set of powers such that all links are successful simultaneously. A classic algorithm for this problem is the fixed-point iteration due to Foschini and Miljanic [8], for which we prove the first bounds on worst-case running times – after roughly O(n logn) rounds all SINR constraints are nearly satisfied. When we try to satisfy each constraint exactly, however, convergence time is infinite. For this case, we design a novel framework for power control using regret learning algorithms and iterative discretization. While the exact convergence times must rely on a variety of parameters, we show that roughly a polynomial number of rounds suffices to make every link successful during at least a constant fraction of all previous rounds.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andrews, M., Dinitz, M.: Maximizing capacity in arbitrary wireless networks in the sinr model: Complexity and game theory. In: Proceedings of the 28th Conference of the IEEE Communications Society, INFOCOM (2009)Google Scholar
  2. 2.
    Arora, S., Hazan, E., Kale, S.: The multiplicative weights update method: a meta algorithm and applications (2005) (manuscript)Google Scholar
  3. 3.
    Asgeirsson, E.I., Mitra, P.: On a game theoretic approach to capacity maximization in wireless networks. In: Proceedings of the 30th Conference of the IEEE Communications Society, INFOCOM (2011)Google Scholar
  4. 4.
    Blum, A., Mansour, Y.: From external to internal regret. J. Mach. Learn. Res. 8, 1307–1324 (2007)MATHMathSciNetGoogle Scholar
  5. 5.
    Dinitz, M.: Distributed algorithms for approximating wireless network capacity. In: Proceedings of the 29th Conference of the IEEE Communications Society (INFOCOM), pp. 1397–1405 (2010)Google Scholar
  6. 6.
    Fanghänel, A., Geulen, S., Hoefer, M., Vöcking, B.: Online capacity maximization in wireless networks. In: Proceedings of the 22nd ACM Symposium on Parallelism in Algorithms and Architectures, pp. 92–99 (2010)Google Scholar
  7. 7.
    Fanghänel, A., Kesselheim, T., Räcke, H., Vöcking, B.: Oblivious interference scheduling. In: Proceedings of the 28th ACM Symposium on Principles of Distributed Computing (PODC), pp. 220–229 (2009)Google Scholar
  8. 8.
    Foschini, G.J., Miljanic, Z.: A simple distributed autonomous power control algorithm and its convergence. IEEE Transactions on Vehicular Technology 42(4), 641–646 (1992)CrossRefGoogle Scholar
  9. 9.
    Goussevskaia, O., Wattenhofer, R., Halldórsson, M.M., Welzl, E.: Capacity of arbitrary wireless networks. In: Proceedings of the 28th Conference of the IEEE Communications Society (INFOCOM), pp. 1872–1880 (2009)Google Scholar
  10. 10.
    Halldórsson, M.M.: Wireless scheduling with power control. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 361–372. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Halldórsson, M.M., Mitra, P.: Wireless capacity with oblivious power in general metrics. In: Proceedings of the 22nd ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1538–1548 (2011)Google Scholar
  12. 12.
    Huang, C.Y., Yates, R.D.: Rate of convergence for minimum power assignment algorithms in cellular radio systems. Wireless Networks 4(4), 223–231 (1998)CrossRefGoogle Scholar
  13. 13.
    Kesselheim, T.: A constant-factor approximation for wireless capacity maximization with power control in the SINR model. In: Proceedings of the 22nd ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1549–1559 (2011)Google Scholar
  14. 14.
    Kesselheim, T., Vöcking, B.: Distributed contention resolution in wireless networks. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 163–178. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Moscibroda, T., Wattenhofer, R.: The complexity of connectivity in wireless networks. In: Proceedings of the 25th Conference of the IEEE Communications Society (INFOCOM), pp. 1–13 (2006)Google Scholar
  16. 16.
    Singh, V., Kumar, K.: Literature survey on power control algorithms for mobile ad-hoc network. Wireless Personal Communications, 1–7 (2010), doi:10.1007/s11277-010-9967-xGoogle Scholar
  17. 17.
    Yates, R.D.: A framework for uplink power control in cellular radio systems. IEEE Journal on Selected Areas in Communications 13(7), 1341–1347 (1995)CrossRefGoogle Scholar
  18. 18.
    Zinkevich, M.: Online convex programming and generalized infinitesimal gradient ascent. In: Proceedings of the 20th International Conference on Machine Learning, pp. 928–936 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Johannes Dams
    • 1
  • Martin Hoefer
    • 1
  • Thomas Kesselheim
    • 1
  1. 1.Department of Computer ScienceRWTH Aachen UniversityGermany

Personalised recommendations