Approximation algorithms for the antenna orientation problem

  • Authors:
  • Evangelos Kranakis;Fraser MacQuarrie;Oscar Morales Ponce

  • Affiliations:
  • School of Computer Science, Carleton University, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;Department of Computing, Chalmers University, Goeteborg, Sweden

  • Venue:
  • FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
  • Year:
  • 2013

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Abstract

We consider the following Antenna Orientation Problem: Given a connected Unit Disk Graph (UDG) formed by n identical omnidirectional sensors, what is the optimal range (or radius) which is necessary and sufficient for a given antenna beamwidth (or angle) φ so that after replacing the omnidirectional sensors by directional antennae of beamwidth φ we can determine an appropriate orientation of each antenna so that the resulting graph is strongly connected? The problem was first proposed and studied in Caragiannis et al. [3] where they showed that the antenna orientation problem can be solved optimally for φ≥8 π/5, and is NP-Hard for φπ/3, where there is no approximation algorithm with ratio less than $\sqrt{3}$, unless P=NP. In this paper we study beamwidth/range tradeoffs for the antenna orientation problem. Namely, for the full range of angles in the interval [0 , 2 π] we compare the antenna range provided by an orientation algorithm to the optimal possible for the given beamwidth. We employ the concept of (2,φ)-connectivity, a generalization of the well-known 2-connectivity, which relates connectivity in the directed graph to the best possible antenna orientation at a given point of the graph and use this to propose new antenna orientation algorithms that ensure improved bounds on the antenna range for given angles and analyze their complexity.