Abstract
Sustaining an operational wireless sensor network (WSN) is challenging due to the persistent need of the battery-powered sensors to be charged from time to time. The procedure of exploiting mobile chargers (MCs) that traverse to the fixed sensors of the network and wirelessly transfer energy in an efficient matter has been considered widely as a promising way to tackle this challenge. 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 meeting the sensor recharge frequency and the schedule of these MCs. It is shown that this optimization problem becomes NP-hard in high-dimensional spaces. Moreover, the special case of the homogeneous recharge frequency of the sensors has already been proven to have a tractable algorithm if we consider whether the 1-dimensional space is a line or a ring. In this work, we seek to find a delicate border between the tractable and the intractable problem space. Specifically, we study the special case of heterogeneous sensors that take frequencies of 1's and 2's (lifetime of 1 and 0.5 time units) on a line, conjecture the special case's 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. Afterwards, we introduce the energy optimization problem of the MCs with the minimized number and solve it optimally. Comprehensive simulation is conducted to verify the efficiency of using our proposed algorithms that minimize the number of MCs.
