On Minimizing the Maximum Sensor Movement for Barrier Coverage of a Line Segment

  • J. Czyzowicz
  • E. Kranakis
  • D. Krizanc
  • I. Lambadaris
  • L. Narayanan
  • J. Opatrny
  • L. Stacho
  • J. Urrutia
  • M. Yazdani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5793)

Abstract

We consider n mobile sensors located on a line containing a barrier represented by a finite line segment. Sensors form a wireless sensor network and are able to move within the line. An intruder traversing the barrier can be detected only when it is within the sensing range of at least one sensor. The sensor network establishes barrier coverage of the segment if no intruder can penetrate the barrier from any direction in the plane without being detected. Starting from arbitrary initial positions of sensors on the line we are interested in finding final positions of sensors that establish barrier coverage and minimize the maximum distance traversed by any sensor. We distinguish several variants of the problem, based on (a) whether or not the sensors have identical ranges, (b) whether or not complete coverage is possible and (c) in the case when complete coverage is impossible, whether or not the maximal coverage is required to be contiguous. For the case of n sensors with identical range, when complete coverage is impossible, we give linear time optimal algorithms that achieve maximal coverage, both for the contiguous and non-contiguous case. When complete coverage is possible, we give an O(n2) algorithm for an optimal solution, a linear time approximation scheme with approximation factor 2, and a (1 + ε) PTAS. When the sensors have unequal ranges we show that a variation of the problem is NP-complete and identify some instances which can be solved with our algorithms for sensors with unequal ranges.

Keywords

Barrier Coverage Detection Intruder Line Segment Optimal Movement Sensors NP-complete PTAS 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • J. Czyzowicz
    • 1
  • E. Kranakis
    • 2
  • D. Krizanc
    • 3
  • I. Lambadaris
    • 4
  • L. Narayanan
    • 5
  • J. Opatrny
    • 5
  • L. Stacho
    • 6
  • J. Urrutia
    • 7
  • M. Yazdani
    • 4
  1. 1.Département d’informatiqueUniversité du Québec en OutaouaisGatineauCanada
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada
  3. 3.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA
  4. 4.Department of Systems and Computer EngineeringCarleton UniversityOttawaCanada
  5. 5.Department of Computer ScienceConcordia UniversityMontréalCanada
  6. 6.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  7. 7.Instituto de MatemáticasUniversidad Nacional Autónoma de México,Área de la investigación cientifica, Circuito Exterior, Ciudad Universitaria, CoyoacánMéxicoMéxico

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