Efficient Algorithms for Max-Weighted Point Sweep Coverage on Lines

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 [Formula: see text] time; our polynomial-time approximation algorithm for the case when sensors have a constant number of velocities achieves approximation ratio [Formula: see text]; for the general case of arbitrary velocities, [Formula: see text] and [Formula: see text] approximation algorithms are presented, respectively, where integer [Formula: see text] is the tradeoff factor between time complexity and approximation ratio.