Mobile Charger Coverage Problem for Specific Heterogeneous Wireless Sensor Networks

One of the main hindrances that wireless sensor networks (WSNs) face is the battery-powered sensors that need to be charged from time to time. Recently, the approach of having mobile chargers (MCs) that travel to the static sensors of the network and transfer energy wirelessly and efficiently has become a promising solution to that hindrance. An optimization problem, called the mobile charger coverage problem, arises naturally to keep all of the sensors alive with an objective of determining both the minimum number of MCs required to meet the sensor recharge frequency and the schedule of these MCs. It is shown that this optimization problem becomes NP-hard in a high-dimensional space, including 2-D space with homogeneous recharging frequency. On the other hand, it is shown that a polynomial-time algorithm exists for sensors with a homogeneous recharge frequency on a 1-dimensional space (line or ring). In this paper, we seek to find a delicate border between the tractable and intractable problem space. Specifically, we study the special case of heterogeneous sensors that take frequencies of 1’s and 2’s (lifetimes of 1 and 0.5 time units) on a line, conjecture its NP-hardness, propose a novel brute-force optimal algorithm, and present a linear-time greedy algorithm that gives a 1.5-approximation solution for the problem. A comprehensive simulation is conducted to verify the efficiency of using our proposed algorithms.