Journal of Combinatorial Optimization

, Volume 25, Issue 2, pp 208–233 | Cite as

Coverage with k-transmitters in the presence of obstacles

  • Brad Ballinger
  • Nadia Benbernou
  • Prosenjit Bose
  • Mirela Damian
  • Erik D. Demaine
  • Vida Dujmović
  • Robin Flatland
  • Ferran Hurtado
  • John Iacono
  • Anna Lubiw
  • Pat Morin
  • Vera Sacristán
  • Diane Souvaine
  • Ryuhei Uehara
Article

Abstract

For a fixed integer k≥0, a k-transmitter is an omnidirectional wireless transmitter with an infinite broadcast range that is able to penetrate up to k “walls”, represented as line segments in the plane. We develop lower and upper bounds for the number of k-transmitters that are necessary and sufficient to cover a given collection of line segments, polygonal chains and polygons.

Keywords

Coverage Guarding Transmitters Art gallery Visibility 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Brad Ballinger
    • 1
  • Nadia Benbernou
    • 2
  • Prosenjit Bose
    • 3
  • Mirela Damian
    • 4
  • Erik D. Demaine
    • 2
  • Vida Dujmović
    • 3
  • Robin Flatland
    • 5
  • Ferran Hurtado
    • 6
  • John Iacono
    • 7
  • Anna Lubiw
    • 8
  • Pat Morin
    • 3
  • Vera Sacristán
    • 6
  • Diane Souvaine
    • 9
  • Ryuhei Uehara
    • 10
  1. 1.Humboldt State UniversityArcataUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA
  3. 3.Carleton UniversityOttawaCanada
  4. 4.Villanova UniversityVillanovaUSA
  5. 5.Siena CollegeLoudonvilleUSA
  6. 6.Universitat Politècnica de CatalunyaBarcelonaSpain
  7. 7.Polytechnic Institute of New York UniversityNew YorkUSA
  8. 8.University of WaterlooWaterlooCanada
  9. 9.Tufts UniversityMedfordUSA
  10. 10.Japan Advanced Institute of Science and TechnologyIshikawaJapan

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