A primal-dual approximation algorithm for the k-prize-collecting minimum power cover problem

In this paper, we introduce the k -prize-collecting minimum power cover problem ( k -PCPC). In this problem, we are given a point set V , a sensor set S on a plane and a parameter k with k ≤ | V | . Each sensor can adjust its power and the covering range of sensor s with power p ( D ( s ,  r ( s )))...

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Vydané v:Optimization letters Ročník 16; číslo 8; s. 2373 - 2385
Hlavní autori: Liu, Xiaofei, Li, Weidong, Xie, Runtao
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2022
Predmet:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Power cover
Approximation algorithm
prize-collection
Primal-dual
ISSN:1862-4472, 1862-4480
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Popis
Shrnutí:In this paper, we introduce the k -prize-collecting minimum power cover problem ( k -PCPC). In this problem, we are given a point set V , a sensor set S on a plane and a parameter k with k ≤ | V | . Each sensor can adjust its power and the covering range of sensor s with power p ( D ( s ,  r ( s ))) is a disk D ( s ,  r ( s )), where r ( s ) is the radius of disk D ( s ,  r ( s )) and p ( D ( s , r ( s ) ) ) = c · r ( s ) α . The k -PCPC determines a disk set F such that at least k points are covered, where the center of any disk in F is a sensor. The objective is to minimize the total power of the disk set F plus the penalty of R , where R is the set of points that are not covered by F . This problem generalizes the well-known minimum power cover problem, minimum power partial cover problem and prize collecting minimum power cover problem. Our main result is to present a novel two-phase primal-dual algorithm for the k -PCPC with an approximation ratio of at most 3 α .
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-021-01831-z