Skip to main content
SpringerLink
Log in

Optimal Sensor Networks for Area Monitoring Using Rotating and Beam Sensors

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript

Abstract

We consider the problem of monitoring the Euclidean plane using rotating sensors with detection sectors and beam sensors. We assume that intruders can appear anywhere at any time and move arbitrarily fast, and may have full knowledge of the sensor network. We require that such intruders be detected within a finite amount of time. We give an optimal network for this problem consisting of a combination of rotating sensors of angle 0 and beam sensors that uses the minimum number of both types of sensors. We show a trade-off between the density of beam sensors needed and the angle of the detection sector of the rotating sensors. Secondly, we give a family of sensor networks using only rotating sensors for the same problem, that demonstrate a trade-off between the detection time and the density of rotating sensors used. We show that the density of rotating sensors required in this case can be significantly reduced by increasing the angle of detection sectors. Finally, we show that our results on the infinite plane can be used to derive sensor networks that monitor some finite regions using a density of sensors that is asymptotically the same, or close to that of the infinite plane case.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Notes

  1. In practice, the intruder may move faster than the speed of the rotating sensor.

References

  1. Balister, P., Bollobas, B., Sarkar, A., Kumar, S.: Reliable density estimates for coverage and connectivity in thin strips of finite length. In: Proc. of the 13th Annual ACM Int. Conference on Mobile Computing and Networking, pp. 75–86 (2007)

    Chapter  Google Scholar 

  2. Bhattacharya, B., Burmester, M., Hu, Y., Kranakis, E., Shi, Q., Wiese, A.: Optimal movement of mobile sensors for barrier coverage of a planar region. Theor. Comput. Sci. 410, 5515–5528 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, A., Kumar, S., Lai, T.H.: Designing localized algorithms for barrier coverage. In: Proc. of the 13th Annual ACM International Conference on Mobile Computing and Networking, pp. 63–74. ACM Press, New York (2007)

    Google Scholar 

  4. Czyzowicz, J., Kranakis, E., Krizanc, D., Lambadaris, I., Narayanan, L., Opatrny, J., Stacho, L., Urrutia, J., Yazdani, M.: On minimizing the maximum sensor movement for barrier coverage of a line segment. In: Proc. of ADHOC-NOW. LNCS, vol. 5793, pp. 194–212. Springer, Berlin (2009)

    Google Scholar 

  5. Czyzowicz, J., Kranakis, E., Krizanc, D., Lambadaris, I., Narayanan, L., Opatrny, J., Stacho, L., Urrutia, J., Yazdani, M.: On minimizing the sum of sensor movements for barrier coverage of a line segment. In: Proc. of ADHOC-NOW. LNCS, vol. 6288, pp. 29–42. Springer, Berlin (2010)

    Google Scholar 

  6. Kumar, S., Lai, T.H., Arora, A.: Barrier coverage with wireless sensors. Wirel. Netw. 13(6), 817–834 (2007)

    Article  Google Scholar 

  7. Huang, C.F., Tseng, Y.C.: The coverage problem in a wireless sensor network. In: Proc. of the 2nd ACM International Conference on Wireless Sensor Networks and Applications, WSNA’03, pp. 115–121. ACM, New York (2003)

    Chapter  Google Scholar 

  8. Li, X., Frey, H., Santoro, N., Stojmenovic, I.: Localized sensor self-deployment with coverage guarantee. ACM SIGMOBILE Mob. Comput. Commun. Rev. 12(2), 50–52 (2008)

    Article  Google Scholar 

  9. Scheibe, K., Huang, F., Klette, R.: Pose estimation of rotating sensors in the context of accurate 3d scene modeling. J. Univers. Comput. Sci. 16(10), 1269–1290 (2010)

    MATH  Google Scholar 

  10. Lee, S., Chung, W.-K.: Rotating IR sensor system for 2.5d sensing. In: Proceedings of the 2006 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 814–819 (2006)

    Chapter  Google Scholar 

  11. Kershner, R.: The number of circles covering a set. Am. J. Math. 61, 665–671 (1939)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Slovak Academy of Sciences, Bratislava, Slovakia

    Stefan Dobrev

  2. Department of Computer Science and Software Engineering, Concordia University, Montreal, QC, Canada

    Lata Narayanan & Jaroslav Opatrny

Authors
  1. Stefan Dobrev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lata Narayanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jaroslav Opatrny
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lata Narayanan.

Additional information

This work was supported by VEGA 2/0136/12 (S. Dobrev) and NSERC Discovery Grants (L. Narayanan, J. Opatrny).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dobrev, S., Narayanan, L. & Opatrny, J. Optimal Sensor Networks for Area Monitoring Using Rotating and Beam Sensors. Theory Comput Syst 54, 622–639 (2014). https://doi.org/10.1007/s00224-013-9483-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00224-013-9483-y

Keywords

Search

Navigation