I. Introduction
Internet of Things (IoTs) [1]–[3] as well as cloud computing [4]–[6] leverage the ubiquity of sensor-equipped devices to collect information at low cost [7], provide a new paradigm for solving the complex sensing applications from the significant demands of critical infrastructure [8], [9]. It is vital to maintain high energy efficiency in data gathering [2], [6]–[8]. To this end, this work focuses on the design of a novel aggregation convergecast cluster structure to minimize both the required number of aggregation time slots (delay, for short) and the energy consumption. In WSNs, convergecast [10]–[12] is one of the most commonly used data aggregation patterns [10]–[12]. The Time Division Multiple Access (TDMA) scheduling approach is adopted in this work because it is more effective than CSMA, especially under medium to high traffic loads [13]. In the convergecast data collection process, the data sensed at all nodes should be aggregated and sent to the sink within the minimal number of time slots and with minimal energy consumption. However, it is well known that the minimal convergecast time (MCT) problem is NP-hard [14]. In addition, Wu et al. [15] have noted that a wireless sensor node will typically wake up periodically to sense the environment and produce new data or to receive or send data to the sink node or other sensor nodes, after which it will return to sleep mode. The corresponding state transition of the processor consumes a significant amount of energy. For instance, the ATMega128L processor of a Mica mote sensor requires 4 ms for start-up, and the RFM radio used by the Mica sensor requires 12 μs to switch between sending and receiving, whereas the raw bit time is 25 μs [15]. Thus, a proposed scheduling scheme should reduce the frequency of state transitions, thereby increasing the network lifetime.