## 1 Introduction
Some events can be more complicated which require some advance detection techniques like supervised or unsupervised techniques from machine learning that is not in scope of our current research. In our approach, we focus on delivering the event-alarms to the system's operators. There are two main advantages for EWSNs in contrast to the typical WSNs; first, in WSNs for recognizing an event all of the information should be transferred to a central processing station and then due to the size of data-set by applying advanced analyzing methods the event information can be extracted which is expensive in time and computational resources. The second advantage is about extending the lifetime of the network by reducing unnecessary communications. Figure 1: Application of WSNs in IoT. Herein, by considering EWSNs for the purpose of monitoring a large operational field such as forest and detecting some specific events such as fire, we employ a grounded mobile-sink for data harvesting. Obviously, the mobile-sink cannot move in an arbitrary trajectory due to physical obstacles. Therefore, we assume that there is a predefined trajectory in the environment. In addition, based on the development scale, practically it is not possible to install the sensor-nodes manually. Thus, we employ a random deployment fashion such as by aircraft. By considering the practical constraints of the environment and the mobile-sink, there is not any possibility for the mobile-sink to visit all of the sensor-nodes one-by-one. Accordingly, the sensor-nodes which are located in proximity of the mobile-sink's trajectory can work as RPs in the network. Based on the above mentioned statements about the intended application scenarios, our main objective is to select a set of RPs in periphery of the predefined trajectory that can satisfy two main expectations which are minimizing energy-consumption of the sensor-nodes and reducing the average data delivery delay in the network. Distributed nature of WSNs and inability of the system to perform any centralized solution is another important consideration in our proposed approach. Therefore, we could achieve the following contributions in our work:  
* Modeling the problem by a Mixed Integer Linear Programming (MILP). * Analyzing the theoretical aspects of the problem and proving its NP-hardness. * Proposing distributed and comprehensive heuristics for constructing a comprehensive framework in our approach. * The first heuristic determines a suitable set of RPs. To cope with the uncertainties in the environment, we designed a Fuzzy Decision System (FDS) model for identifying the potentiality of a sensor-node for becoming a RP. * After selecting the RPs, our second heuristic attempts to find appropriate locations for the mobile-sink to stop and collect the data from the sensor-nodes which are called \"sojourn locations\". * And the third heuristic constructs routing trees for the sensor-nodes which cannot contact with the mobile-sink directly. These sensor-nodes transfer their data to the related RP. * Our experimental results prove the effectiveness of our approach. The rest of the paper is organized as follows. Section 2 discusses about some of the prominent related works. Section 3 summarizes the essential preliminaries for our work. Section 4 introduces the problem and its constraints in the formal form. Section 5 proposes our three heuristics to construct a comprehensive framework. Section 6 presents the numerical experiments. And finally Section 7 concludes this paper.