## Abstract

As an important application of wireless sensor networks (WSNs), deployment of mobile sensors to periodically monitor (sweep cover) a set of points of interest (PoIs) arises in various applications, such as environmental monitoring and data collection. For a set of PoIs in an Eulerian graph, the point sweep coverage problem of deploying the fewest sensors to periodically cover a set of PoIs is known to be Non-deterministic Polynomial Hard (NP-hard), even if all sensors have the same velocity. In this paper, we consider the problem of finding the set of PoIs on a line periodically covered by a given set of mobile sensors that has the maximum sum of weight. The problem is first proven NP-hard when sensors are with different velocities in this paper. Optimal and approximate solutions are also presented for sensors with the same and different velocities, respectively. For M sensors and N PoIs, the optimal algorithm for the case when sensors are with the same velocity runs in O(MN) time; our polynomial-time approximation algorithm for the case when sensors have a constant number of velocities achieves approximation ratio^{1}2; for the general case of arbitrary 1 velocities,_{2α} and^{1}2 (1 − 1/e) approximation algorithms are presented, respectively, where integer α ≥ 2 is the tradeoff factor between time complexity and approximation ratio.

Original language | English |
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Article number | 1457 |

Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | Sensors |

Volume | 21 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2 Feb 2021 |

Externally published | Yes |

## Keywords

- Approximation algorithm
- Integer programming
- Mobile sensors
- Sweep coverage
- WSN