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Journal of Combinatorial Optimization

, Volume 32, Issue 4, pp 985–1001 | Cite as

\((\alpha , \tau )\)-Monitoring for event detection in wireless sensor networks

  • Ran BiEmail author
  • Jianzhong Li
  • Hong Gao
  • Yingshu Li
Article
  • 174 Downloads

Abstract

Detecting abnormal events is one of the fundamental issues in wireless sensor networks (WSNs). In this paper, we investigate \((\alpha ,\tau )\)-monitoring in WSNs. For a given monitored threshold \(\alpha \), we prove that (i) the tight upper bound of \(\Pr [{S(t)} \ge \alpha ]\) is \(O\left( {\exp \left\{ { - n\ell \left( {\frac{\alpha }{{nsup}},\frac{{\mu (t)}}{{nsup}}} \right) } \right\} } \right) \), if \(\mu (t) < \alpha \); and (ii) the tight upper bound of \(\Pr [{S(t)} \le \alpha ]\) is \(O\left( {\exp \left\{ { - n\ell \left( {\frac{\alpha }{{nsup}},\frac{{\mu (t)}}{{nsup}}} \right) } \right\} } \right) \), if \(\mu (t) > \alpha \), where \(\Pr [X]\) is the probability of random event \(X,\, S(t)\) is the sum of the monitored area at time \(t,\, n\) is the number of the sensor nodes, \(sup\) is the upper bound of sensed data, \( \mu (t)\) is the expectation of \(S(t)\), and \(\ell ({x_1},{x_2}) = {x_1}\ln \left( {\frac{{{x_1}}}{{{x_2}}}} \right) + (1 - {x_1})\ln \left( {\frac{{1 - {x_1}}}{{1 - {x_2}}}} \right) \). An instant \((\alpha ,\tau )\)-monitoring scheme is then developed based on the upper bound. Moreover, approximate continuous \((\alpha , \tau )\)-monitoring is investigated. We prove that the probability of false negative alarm is \(\delta \), if the sample size is Open image in new window for a given precision requirement, where Open image in new window is the Open image in new window fractile of a standard normal distribution. Finally, the performance of the proposed algorithms is validated through experiments.

Keywords

Monitoring Distributed algorithm Sensor networks 

Notes

Acknowledgments

This work is supported in part by the National Grand Fundamental Research 973 Program of China under Grant 2012CB316200, the Key Program of the National Natural Science Foundation of China under Grant 61033015, and 60933001, the Major Program of National Natural Science Foundation of China under Grant 61190115.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyHarbin Institute of TechnologyHarbinChina
  2. 2.Department of Computer ScienceGeorgia State UniversityAtlantaUSA

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