  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.
