Efficient Algorithms for Max-Weighted Point Sweep Coverage on Lines

• Published in: Sensors (Basel, Switzerland) Vol. 21; no. 4; p. 1457
• Main Authors: Liang, Dieyan, Shen, Hong
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI 19.02.2021; MDPI AG
• Subjects: approximation algorithm; combinatorial mathematics; mobile sensors; sweep coverage; WSN; approximation algorithm; WSN; combinatorial mathematics; mobile sensors; sweep coverage
• ISSN: 1424-8220; 1424-8220
• DOI: 10.3390/s21041457

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 sensors and 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 12; for the general case of arbitrary velocities, 12α and 12(1-1/e) approximation algorithms are presented, respectively, where integer α≥2 is the tradeoff factor between time complexity and approximation ratio.