Maximum Interference of Random Sensors on a Line

  • Evangelos Kranakis
  • Danny Krizanc
  • Lata Narayanan
  • Ladislav Stacho
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6058)


Consider n sensors whose positions are represented by n uniform, independent and identically distributed random variables assuming values in the open unit interval (0,1). A natural way to guarantee connectivity in the resulting sensor network is to assign to each sensor as range the maximum of the two possible distances to its two neighbors. The interference at a given sensor is defined as the number of sensors that have this sensor within their range. In this paper we prove that the expected maximum interference is Ω(ln ln n), and that for any ε> 0, it is O((ln n)1/2 + ε ).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abay, A.: Extremes of Interarrival Times of a Poisson Process under Conditioning. Applicationes Mathematicae 23(1), 73–82 (1995)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: A first course in order statistics. John Wiley & Sons, Chichester (1992)zbMATHGoogle Scholar
  3. 3.
    Bilo, D., Proletti, G.: On the complexity of minimizing interference in ad hoc and sensor networks. Theoretical Computer Science 402, 43–55 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Buchin, K.: Minimizing the maximum interference is hard, arXiv:0802.2134 (February 2008)Google Scholar
  5. 5.
    Burkhart, M., Wattenhofer, R., Zollinger, A.: Does topology control reduce interference? In: Proceedings of the 5th ACM International Symposium on Mobile ad hoc Networking and Computing, pp. 9–19. ACM, New York (2004)CrossRefGoogle Scholar
  6. 6.
    Darling, D.A.: On a class of problems related to the random division of an interval. Ann. Math. Statist. 24, 239–253 (1953)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Transactions on Information Theory 46(2), 388–404 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Halldórsson, M.M., Tokuyama, T.: Minimizing interference of a wireless ad-hoc network in a plane. Theoretical Computer Science 402(1), 29–42 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Jain, K., Padhye, J., Padmanabhan, V.N., Qiu, L.: Impact of Interference on Multi-Hop Wireless Network Performance. Wireless Networks 11(4), 471–487 (2005)CrossRefGoogle Scholar
  10. 10.
    Locher, T., von Rickenbach, P., Wattenhofer, R.: Sensor Networks Continue to Puzzle: Selected Open Problems. In: Rao, S., Chatterjee, M., Jayanti, P., Murthy, C.S.R., Saha, S.K. (eds.) ICDCN 2008. LNCS, vol. 4904, p. 25. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Moscibroda, T., Wattenhofer, R.: Minimizing interference in ad hoc and sensor networks. In: Proceedings of the 2005 Joint Workshop on Foundations of Mobile Computing, pp. 24–33. ACM, New York (2005)CrossRefGoogle Scholar
  12. 12.
    Penrose, M.D.: The longest edge of the random minimal spanning tree. Annals of Applied Probability 7, 340–361 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Pyke, R.: Spacings. Journal of the Royal Statistical Society. Series B (Methodological) 27(3), 395–449 (1965)zbMATHMathSciNetGoogle Scholar
  14. 14.
    von Rickenbach, P., Schmid, S., Wattenhofer, R., Zollinger, A.: A Robust Interference Model for Wireless Ad-Hoc Networks. In: Proc. 5th IEEE International Workshop on Algorithms for Wireless, Mobile, Ad-Hoc and Sensor Networks, WMAN (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Evangelos Kranakis
    • 1
  • Danny Krizanc
    • 2
  • Lata Narayanan
    • 3
  • Ladislav Stacho
    • 4
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA
  3. 3.Department of Computer Science and Software EngineeringConcordia UniversityMontrealCanada
  4. 4.Department of MathematicsSimon Fraser UniversityBurnabyCanada

Personalised recommendations