Coverage restricted to an angle

  • Authors:
  • Manuel Abellanas;Antonio L. Bajuelos;Ferran Hurtado;InêS Matos

  • Affiliations:
  • Facultad de Informática (UPM), Campus de Montegancedo, 28660 Boadilla del Monte, Madrid, Spain;Department de Matemática (UA), Campus Universitário de Santiago, 3810-193 Aveiro, Portugal;Department de Matemítica Aplicada II (UPC), Edifici . C. Jordi Girona, 1-3, 08034 Barcelona, Spain;Department de Matemática (UA), Campus Universitário de Santiago, 3810-193 Aveiro, Portugal and Department de Matemítica Aplicada II (UPC), Edifici . C. Jordi Girona, 1-3, 08034 Barc ...

  • Venue:
  • Operations Research Letters
  • Year:
  • 2011

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Abstract

Given a set S of n antennas and point q on the plane, q is @a-covered by S if @?s"i,s"j@?S such that the angle @?(s"i,q,s"j)=@a. It is shown how to minimise the transmission range of S to @a-cover a point in O(n) time and space, and how to construct the @p2-covered region in O(nlogn) time and O(n) space. Finally, this paper introduces the Coverage Voronoi diagram and an algorithm to construct it in O(n^4logn) time.