## 1 Introduction  
Wireless Sensor Networks (WSNs) have many potential applications, which include environmental monitoring, tracking, healthcare, surveillance, smart homes and so forth [1; 2; 3; 4]. Since sensors are battery powered, prolonging the network lifetime of WSNs is crucial for the usage of sensors in this wide range of applications. Communication is one of the major sources of energy consumption. With limited transmission range, sensors typically deliver their readings to the sink in a multi-hop manner. This behavior will raise the problem of unbalanced energy since the sensors closer to the sink have heavier data-relaying workloads and thus exhaust their energies much faster than the more distant sensors [5, 6, 7]. As a result, the network will be partitioned and hence the sink can become unreachable by other sensors. Instead of constructing a data collection tree from a fixed sink to all sensors, a number of studies [8, 9, 10, 11] have employed a mobile data collector (or mobile sink) moving along some predefined trajectory to migrate the data-relaying workload from one sensor to another. In [8] and [9] a trajectory which enables the mobile sink to directly communicate with sensors was constructed. However, the length of trajectory increases with the size of the monitoring region. This is because the constructed trajectory has to pass through the transmission range of each sensor. As a result, sensors have to wait for a long time to be visited by mobile sink again, leading to a long visit latency. [PERSON] _et al_. [10] selected some sensors as the tree roots and then constructed a tree from all the other sensors to each root. By visiting the selected roots in turn, a mobile sink can collect the readings generated by all sensors based on the constructed tree in a multi-hop manner. Compared to studies [8] and [9], the scheme proposed in [10] significantly reduces the trajectory length of the mobile sink. Nevertheless, the data-relaying workloads of roots are higher than those of the other sensors, resulting in an energy-unbalanced problem. [PERSON] _et al_. [11] considered a circular monitoring region. All sensors are assumed to be uniformly deployed over the monitoring region. As shown in Figure 1, the mobile sink whose transmission range is \(r\) moves along the boundary of the monitoring region to collect readings. The sensors located at the boundary, called _boundary sensors_, can be visited by mobile sink while the remaining sensors have to deliver their readings to the mobile sink in a multi-hop manner due to the limited transmission range. To forward the collected readings to the sink, the boundary sensors will receive and store the readings and then wait for mobile sink to pass through their transmission ranges. However, sensors closer to the center of the monitoring region would have much fewer data-relaying workloads than the boundary sensors. For example, as shown in Figure 1, each of red nodes only needs to deliver their own readings to their neighbors without any data-relaying workloads. Consequently, the boundary sensors and the red nodes have different energy consumptions, leading to an energy-unbalance  
Figure 1: The red nodes and boundary sensors are energy-unbalanced. problem. This paper proposes an Energy-Balanced Data Collection mechanism, called _EBDC_, which determines a trajectory such that the data-relaying workloads of all sensors can be totally balanced. Similar to the network environment of study [11], this paper considers a circular monitoring region which has been geographically partitioned into a number of circular tracks. To balance the data-relaying workloads, the mobile sink moves along different tracks with predefined sweep repetitions. At any given time, each sensor is able to derive the track where the mobile sink is visiting currently. Therefore, each sensor can send its reading to the appropriate neighbor such that the reading can reach the mobile sink in a multi-hop manner. Furthermore, the proposed _EBDC_ mechanism can be applied to a wide range of applications.