Approximation algorithms for maximum weighted target cover problem with distance limitations

Jianhong Jin, Yingli Ran () and Zhao Zhang ()
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Jianhong Jin: Zhejiang Normal University
Yingli Ran: Zhejiang Normal University
Zhao Zhang: Zhejiang Normal University

Journal of Combinatorial Optimization, 2024, vol. 47, issue 4, No 7, 14 pages

Abstract: Abstract In this paper, we study approximation algorithms for the problem of maximum weighted target cover with distance limitations (MaxWTCDL). Given n targets $$T=\left\{ t_{1},t_{2},\ldots ,t_{n}\right\} $$ T = t 1 , t 2 , … , t n on the plane and m mobile sensors $$S=\left\{ s_{1},s_{2},\ldots ,s_{m}\right\} $$ S = s 1 , s 2 , … , s m randomly deployed on the plane, each target $$t_i$$ t i has a weight $$w_{i}$$ w i and the sensing radius of the mobile sensors is $$r_{s}$$ r s , suppose there is a movement distance constraint b for each sensor and a total movement distance constraint B, where $$B>b$$ B > b , the goal of MaxWTCDL is to move the mobile sensors within the distance constraints b and B to maximize the weight of covered targets. We present two polynomial time approximation algorithms. One is greedy-based, achieving approximation ratio $$\frac{1}{2v}$$ 1 2 v in time $$O(mn^2)$$ O ( m n 2 ) , where . The other is LP-based, achieving approximation ratio $$\frac{1}{v}(1-e^{-1})$$ 1 v ( 1 - e - 1 ) in time $$T_{LP}$$ T LP , where $$T_{LP}$$ T LP is the time needed to solve the linear program.

Keywords: Target coverage; Distance constraint; Approximation algorithm (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01166-2

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