Sweep coverage provides solutions for the applications in wireless sensor networks, where
periodic monitoring is sufficient instead of continuous monitoring. The objective of the
sweep coverage problem is to minimize the number of sensors required in order to
guarantee sweep coverage for a given set of points of interest on a plane. Instead of using
only mobile sensors for sweep coverage, use of both static and mobile sensors can be more
effective in terms of energy utilization. In this paper, we introduce two variations in sweep
coverage problem, where energy consumption by the sensors is taken into consideration.
First, an energy efficient sweep coverage problem is proposed, where the objective is to
minimize energy consumption by a set of sensors (mobile and/or static) with guaranteed
sweep coverage. We prove that the problem is NP-hard and cannot be approximated
within a factor of 2. An 8-approximation algorithm is proposed to solve the problem. A
2-approximation algorithm is also proposed for a special case. Second, an energy restricted
sweep coverage problem is proposed, where the objective is to find the minimum number
of mobile sensors to guarantee sweep coverage subject to the condition that the energy
consumption by a mobile sensor in a given time period is bounded. We propose a (5+ 2
α )-
approximation algorithm to solve this NP-hard problem.