Coverage with k-transmitters in the presence of obstacles

Authors:
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
Affiliations:
Humboldt State University, Arcata, USA;Massachusetts Institute of Technology, Cambridge, USA;Carleton University, Ottawa, Canada;Villanova University, Villanova, USA;Massachusetts Institute of Technology, Cambridge, USA;Carleton University, Ottawa, Canada;Siena College, Loudonville, USA;Universitat Politècnica de Catalunya, Barcelona, Spain;Polytechnic Institute of New York University, New York, USA;University of Waterloo, Waterloo, Canada;Carleton University, Ottawa, Canada;Universitat Politècnica de Catalunya, Barcelona, Spain;Tufts University, Medford, USA;Japan Advanced Institute of Science and Technology, Ishikawa, Japan
Venue:
Journal of Combinatorial Optimization
Year:
2013

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Abstract

For a fixed integer k驴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.