## 1 Introduction  
Wireless Sensor Networks (WSNs) equipped with extremely small, low cost sensors that possess sensing, signal processing and wireless communication capacities are highly capable of performing monitoring applications. In conventional WSNs, a dense static sensor deployment is implicitly required. Subsequently, there arises a fundamental problem in WSNs with static topology: the non-uniformity of energy consumption among the sensors. In fact, the nearer a sensor lies in relation to the sink, the faster its energy will be depleted. In case of sensor failure or malfunction around a sink, the network connectivity and coverage may not be guaranteed. Intuitively, there are two solutions to the above problems. On the one hand, if some sensors withdraw from the network due to energy exhaustion such that the network loses the necessary connectivity and sensing coverage, other supplementary sensors must be deployed. On the other hand, the sensors should be capable of finding and reaching the sink in possibly different positions, whether there are multiple sinks or the sink is able to change its location. The first approach is frequently related to the design of mobile robotics, therefore we will focus our efforts on the second one: the use of multiple mobile sinks. It is envisaged that in the near future, very large scale networks consisting of both mobile and static nodes will be deployed for mission-critical applications ranging from environmental monitoring to emergency search-and-rescue operations. Energy is identified as the most crucial resource in sensor networks due to the difficulty of recharging batteries of thousands of devices in remote or hostile environments. In this paper, we show that it is possible to achieve considerable savings in energy consumption expended on communication to mobile sinks at the expense of a moderate increase in message delivery delay. Exploration of this trade-off is the main principle that underlies the design of our algorithm.  
It is known to all that the deployment should result in configurations that not only provide good \"sensor coverage\" but also satisfy certain global (e.g., network connectivity) constraints. In [1] sensor coverage problems were studied and categorized into three types: _area coverage_, _point coverage_, and _barrier coverage_. The objective of the first, area coverage, is to maximize the coverage for a region of interest. The objective of point coverage is similar, but it is to cover a set of points. The latter, barrier coverage, aims to minimize the probability of undetected penetration through a sensor network. The choice of using a particular coverage measurement depends on the purpose of a sensor network. For instance, if the purpose is to monitor moving objects in a field, barrier coverage is more suitable. To measure barrier coverage, [2] defined the worst- and best-case coverage. They proposed two centralized algorithms to solve these problems. The best-case coverage algorithm was later extended to a distributed localized one in [3]. Based on the optimal multi-hop network coverage solution, we investigated detecting an event where sensors may need to aggregate the data. Therefore, a Mobile Sink (MS) was introduced into the network clustered in a similar way as in our previous work [4]. Regarding modeling the energy performance, in the energy model for gathered data transmission, MS mobility and load balancing critical factors.