Point Sweep Coverage on Path

An important application of wireless sensor networks is the deployment of mobile sensors to periodically monitor (cover) a set of points of interest (PoIs). The problem of Point Sweep Coverage is to deploy fewest sensors to periodically cover the set of PoIs. For PoIs in a Eulerian graph, this problem is known NP-Hard even if all sensors are with uniform velocity. In this paper, we study the problem when PoIs are on a line and prove that the decision version of the problem is NP-Complete if the sensors are with different velocities. We first formulate the problem of Max-PoI sweep coverage on path (MPSCP) to find the maximum number of PoIs covered by a given set of sensors, and then show it is NP-Hard. We also extend it to the weighted case, Max-Weight sweep coverage on path (MWSCP) problem to maximum the sum of the weight of PoIs covered. For sensors with uniform velocity, we give a polynomial-time optimal solution to MWSCP. For sensors with constant kinds of velocities, we present a $\frac{1}{2}$-approximation algorithm. For the general case of arbitrary velocities, we propose two algorithms. One is a $\frac{1}{2\alpha}$-approximation algorithm family scheme, where integer $\alpha\ge2$ is the tradeoff factor to balance the time complexity and approximation ratio. The other is a $\frac{1}{2}(1-1/e)$-approximation algorithm by randomized analysis

Approximation Algorithms for Barrier Sweep Coverage

Time-varying coverage, namely sweep coverage is a recent development in the area of wireless sensor networks, where a small number of mobile sensors sweep or monitor comparatively large number of locations periodically. In this article we study barrier sweep coverage with mobile sensors where the barrier is considered as a finite length continuous curve on a plane. The coverage at every point on the curve is time-variant. We propose an optimal solution for sweep coverage of a finite length continuous curve. Usually energy source of a mobile sensor is battery with limited power, so energy restricted sweep coverage is a challenging problem for long running applications. We propose an energy restricted sweep coverage problem where every mobile sensors must visit an energy source frequently to recharge or replace its battery. We propose a $\frac{13}{3}$-approximation algorithm for this problem. The proposed algorithm for multiple curves achieves the best possible approximation factor 2 for a special case. We propose a 5-approximation algorithm for the general problem. As an application of the barrier sweep coverage problem for a set of line segments, we formulate a data gathering problem. In this problem a set of mobile sensors is arbitrarily monitoring the line segments one for each. A set of data mules periodically collects the monitoring data from the set of mobile sensors. We prove that finding the minimum number of data mules to collect data periodically from every mobile sensor is NP-hard and propose a 3-approximation algorithm to solve it