Strong Connectivity in Sensor Networks with Given Number of Directional Antennae of Bounded Angle

  • Stefan Dobrev
  • Evangelos Kranakis
  • Danny Krizanc
  • Jaroslav Opatrny
  • Oscar Morales Ponce
  • Ladislav Stacho
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6509)

Abstract

Given a set S of n sensors in the plane we consider the problem of establishing an ad hoc network from these sensors using directional antennae. We prove that for each given integer 1 ≤ k ≤ 5 there is a strongly connected spanner on the set of points so that each sensor uses at most k such directional antennae whose range differs from the optimal range by a multiplicative factor of at most \(2 \cdot \sin(\frac{\pi}{k+1})\). Moreover, given a minimum spanning tree on the set of points the spanner can be constructed in additional O(n) time. In addition, we prove NP completeness results for k = 2 antennae.

Keywords

Antenna Directional Antenna Minimum Spanning Tree Sensors Spanner Strongly Connected 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Stefan Dobrev
    • 1
  • Evangelos Kranakis
    • 2
  • Danny Krizanc
    • 3
  • Jaroslav Opatrny
    • 4
  • Oscar Morales Ponce
    • 2
  • Ladislav Stacho
    • 5
  1. 1.Institute of MathematicsSlovak Academy of SciencesBratislavaSlovak Republic
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada
  3. 3.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA
  4. 4.Department of Computer ScienceConcordia UniversityMontréalCanada
  5. 5.Department of MathematicsSimon Fraser UniversityBurnabyCanada

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