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Target Coverage with Minimum Number of Camera Sensors

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Combinatorial Optimization and Applications (COCOA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13135))

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Abstract

With the development of the smart city, camera sensors have attracted more and more research interests from both academic researchers and industrial engineers. Given a set of points of interests (POI) and a set of cameras, practical applications require to deploy these cameras with the minimum cost so that these POIs can be fully covered by these cameras. In this paper, we study a problem called Min-Num LTC-CS, which is, given a set of POIs located on a line segment and a set of cameras distributed on the plane, to choose a minimum number of cameras so that these POIs can be fully covered by the sensing ranges of these cameras. We first propose a grouping algorithm by grouping the POIs according to whether they can be covered by the same camera with certain rotation angle and then construct a graph using these POI groups. We show that there exists a feasible constrained st-flow if and only if there exists a subset of cameras that can completely cover these POIs. Then we propose an LP formulation for the constrained flow problem and prove that any basic solution of the LP formulation is integral, which consequently leads to an optimal solution to Min-Num LTC-CS by solving this LP formulation. Lastly, extensive numerical experiments are conducted to demonstrate the practical performance of our algorithms.

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Acknowledgements

The authors are supported by Natural Science Foundation of China (No. 61772005), Outstanding Youth Innovation Team Project for Universities of Shandong Province (No. 2020KJN008), Natural Science Foundation of Fujian Province (No. 2020J01845) and Educational Research Project for Young and Middle-aged Teachers of Fujian Provincial Department of Education (No. JAT190613).

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Authors and Affiliations

  1. Fuzhou University, Fuzhou, China

    Pei Yao, Longkun Guo & Huihong Peng

  2. South China Agricultural University, Guangzhou, China

    Shuangjuan Li

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  1. Pei Yao
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  2. Longkun Guo
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  3. Shuangjuan Li
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  4. Huihong Peng
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Corresponding author

Correspondence to Longkun Guo .

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Editors and Affiliations

  1. University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. University of New Brunswick, Fredericton, NB, Canada

    Donglei Du

  3. Tianjin University of Technology, Tianjin, China

    Chenchen Wu

  4. Beijing University of Technology, Beijing, China

    Dachuan Xu

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Yao, P., Guo, L., Li, S., Peng, H. (2021). Target Coverage with Minimum Number of Camera Sensors. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_2

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  • DOI: https://doi.org/10.1007/978-3-030-92681-6_2

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  • Print ISBN: 978-3-030-92680-9

  • Online ISBN: 978-3-030-92681-6

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