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A unified approach to approximate partial, prize-collecting, and budgeted sweep cover problems

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Abstract

In a sweep cover problem, mobile sensors move around to collect information from positions of interest (PoIs) periodically and timely. A PoI is sweep-covered if it is visited at least once in every time period t. In this paper, we study approximation algorithms on three types of sweep cover problems. The partial sweep cover problem (PSC) aims to use the minimum number of mobile sensors to sweep-cover at least a given number of PoIs. The prize-collecting sweep cover problem aims to minimize the cost of mobile sensors plus the penalties on those PoIs that are not sweep-covered. The budgeted sweep cover problem (BSC) aims to use a budgeted number N of mobile sensors to sweep-cover as many PoIs as possible. We propose a unified approach which can yield approximation algorithms for PSC and PCSC within approximation ratio at most 8, and a bicriteria \((4,\frac{1}{2})\)-approximation algorithm for BSC (that is, no more than 4N mobile sensors are used to sweep-cover at least \(\frac{1}{2}opt\) PoIs, where opt is the number of PoIs that can be sweep-covered by an optimal solution). Furthermore, our results for PSC and BSC can be extended to their weighted version, and our algorithm for PCSC answers a question proposed in Liang et al. (Theor Comput Sci, 2022) on PCSC.

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Acknowledgements

This research is supported by National Natural Science Foundation of China (U20A2068), Zhejiang Provincial Natural Science Foundation of China (LD19A010001) and NSF of USA under Grant III-1907472.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Wei Liang & Zhao Zhang

  2. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA

    Ding-Zhu Du

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  1. Wei Liang
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  2. Zhao Zhang
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  3. Ding-Zhu Du
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Correspondence to Zhao Zhang or Ding-Zhu Du.

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Liang, W., Zhang, Z. & Du, DZ. A unified approach to approximate partial, prize-collecting, and budgeted sweep cover problems. Optim Lett 18, 575–589 (2024). https://doi.org/10.1007/s11590-023-02008-6

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