On minimizing the sum ofensor movements for barrier coverage of a line segment

Authors:
Jurek Czyzowicz;Evangelos Kranakis;Danny Krizanc;Ioannis Lambadaris;Lata Narayanan;Jaroslav Opatrny;Ladislav Stacho;Jorge Urrutia;Mohammadreza Yazdani
Affiliations:
Département d'informatique, Université du Québec en Outaouais, Gatineau, QC, Canada;School of Computer Science, Carleton University, Ottawa, ON, Canada;Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT;Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, Canada;Department of Computer Science, Concordia University, Montréal, QC, Canada;Department of Computer Science, Concordia University, Montréal, QC, Canada;Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada;Instituto de Matemáticas, Universidad Nacional Autónoma de México, México, D.F. México;Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, Canada
Venue:
ADHOC-NOW'10 Proceedings of the 9th international conference on Ad-hoc, mobile and wireless networks
Year:
2010

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Abstract

A set of sensors establishes barrier coverage of a given line segment if every point of the segment is within the sensing range of a sensor. Given a line segment I, n mobile sensors in arbitrary initial positions on the line (not necessarily inside I) and the sensing ranges of the sensors, we are interested in finding final positions of sensors which establish a barrier coverage of I so that the sum of the distances traveled by all sensors from initial to final positions is minimized. It is shown that the problem is NP complete even to approximate up to constant factor when the sensors may have different sensing ranges. When the sensors have an identical sensing range we give several efficient algorithms to calculate the final destinations so that the sensors either establish a barrier coverage or maximize the coverage of the segment if complete coverage is not feasible while at the same time the sum of the distances traveled by all sensors is minimized. Some open problems are also mentioned.