Advertisement

Coping with Interference: From Maximum Coverage to Planning Cellular Networks

  • David Amzallag
  • Joseph (Seffi) Naor
  • Danny Raz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4368)

Abstract

Cell planning includes planning a network of base stations providing a coverage of the service area with respect to current and future traffic requirements, available capacities, interference, and the desired quality-of-service. This paper studies cell planning under budget constraints through a very close-to-practice model. This problem generalizes several problems such as budgeted maximum coverage, budgeted unique coverage, and the budgeted version of the facility location problem.

We present the first study of the budgeted cell planning problem. Our model contains capacities, non-uniform demands, and interference that are modeled by a penalty-based mechanism that may reduce the contribution of a base station to a client as a result of simultaneously covering this client by other base stations. We show that this very general problem is NP-hard to approximate and thus we define a restrictive version of the problem that covers all interesting practical scenarios. We show that although this variant remains NP-hard, it can be approximated within a factor of \(\frac{e-1}{2e-1}\) of the optimum.

Keywords

Approximation Algorithm Cellular Network Facility Location Facility Location Problem Cell Planning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ageev, A., Sviridenko, M.: Approximation algorithms for maximum coverage and max cut with given sizes of parts. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds.) IPCO 1999. LNCS, vol. 1610, pp. 17–30. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Amzallag, D., Engelberg, R., Naor, J., Raz, D.: Approximation algorithms for cell planning problems (2006) (Manuscript) Google Scholar
  3. 3.
    Amzallag, D., Livschitz, M., Naor, J., Raz, D.: Cell planning of 4G cellular networks: Algorithmic techniques, and results. In: Proceedings of the 6th IEE International Conference on 3G & Beyond (3G 2005), pp. 501–506 (2005)Google Scholar
  4. 4.
    Chekuri, C., Khanna, S., Shepherd, F.B.: The all-or-nothing multicommodity flow problem. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pp. 156–165 (2004)Google Scholar
  5. 5.
    Demaine, E.D., Feige, U., Hajiaghayi, M., Salavatipour, M.R.: Combination can be hard: Approximability of the unique coverage problem. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 162–171 (2006)Google Scholar
  6. 6.
    Feige, U.: A threshold of ln n for approximating set cover. J. ACM 45, 634–652 (1998)MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Glaßer, C., Reith, S., Vollmer, H.: The complexity of base station positiong in cellular networks. In: Workshop on Approximation and Randomized Algorithms in Communication Networks, pp. 167–177 (2000)Google Scholar
  8. 8.
    Hochbaum, D.: Heuristics for the fixed cost median problem. Mathematical Programming 22(2), 148–162 (1982)MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Kahn, J., Linial, N., Samorodnitsky, A.: Inclusion-exclusion: exact and approximate. Combinatorica 16, 465–477 (1996)MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Khuller, S., Moss, A., Naor, J.: The budgeted maximum coverage problem. Information Processing Letters 70, 39–45 (1999)MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Linial, N., Nisan, N.: Approximate inclusion-exclusion. Combinatorica 10, 349–365 (1990)MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Sviridenko, M.: A note on maximizing a submodular set function subject to knapsack constraint. Operations Research Letters 32, 41–43 (2004)MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • David Amzallag
    • 1
  • Joseph (Seffi) Naor
    • 1
  • Danny Raz
    • 1
  1. 1.Computer Science DepartmentTechnion - Israel Institute of TechnologyHaifaIsrael

Personalised recommendations