Graph Coloring Inspired Approximate Algorithm for Wireless Energy Redistribution in WSNs

As a new topic attracting research efforts recently, the Wireless Power Transfer based Energy ReDistribution (WPTERD) problem is targeted for finding energy transmission schedules satisfying the nodes' energy expectations, meanwhile achieving minimum energy loss and shortest time span. In this paper, we propose a two-step approach for WPTERD by dividing it into two sub-problems named WPTERD-Egy and WPTERD-Time, which focus on the optimization in energy loss and in time span respectively. Based on some proved properties, the WPTERD-Egy problem is transformed to a Linear Programming problem and thus an optimal time-length list of the nodes' energy transmissions achieving minimum energy loss can be obtain easily. For that WPTERD-Time is NP-hard, we propose an approximate algorithm by exploiting the core idea of the well-known least-degree-last graph coloring algorithm, and prove its approximation ratios respectively for 2D and 3D WSNs. Combining the two steps, we construct our Graph Coloring inspired Energy-Time Decoupling (GCEgyTimeD) algorithm for WPTERD. Numerical simulations validate GCEgyTimeD's ability in returning a schedule with minimum energy loss and with time span within 20% of the optimal value. Simulation results also show that GCEgyTimeD outperforms a representative flow-based algorithm in terms of the tested performance metrics.