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The benefits of using mobile sinks or data mules for data collection in Wireless Sensor Network (WSN) have been studied in several works. However, most of them consider only the WSN limitations and sensor nodes having no more than one data packet to transmit. This paper considers each sensor node having a relatively larger volume of data stored in its memory. That is, they have several data packets to send to sink. We also consider a drone with hovering capability, such as a quad-copter, as a mobile sink to gather this data. Hence, the mobile collector eventually has to hover to guarantee that all data will be received. Drones, however, have a limited power supply that restricts their flying time. Hence, the drone’s energy cost must also be considered to increase the amount of collected data from the WSN. This work investigates the problem of determining the best drone tour for big data gathering in a WSN. We focus on minimizing the overall drone flight time needed to collect all data from the WSN. We propose an algorithm to create a subset of sensor nodes to send data to the drone during its movement and, consequently, reduce its hovering time. The proposed algorithm guarantees that the drone will stay a minimum time inside every sensor node’s radio range. Our experimental results showed that the proposed algorithm surpasses, by up to 30%, the state-of-the-art heuristics’ performance in finding drone tours in this type of scenario.