## 1 Introduction  
Wireless sensor networks (WSNs) consist of a number of spatially-distributed autonomous devices using sensors to monitor physical or environmental conditions. They are multi-functional, low-cost and low-power networks and rely on communications among nodes or from sensor nodes to one or more sink nodes. Sink nodes, sometimes called coordinator nodes or root nodes, may be more robust and have larger processing capacity than the other nodes. Sensor networks can be widely used in various environments, sometimes hostile. Some of the many applications of WSNs are: the medical field, agriculture, monitoring and detection, automation and data mining [1]. The most notable issues regarding WSNs are the difficulty in transmitting information in a wireless environment, as well as the energy costs implied. The signal fades, obstacles, channel occupancy and interference with other devices motivate the use of powerful mechanisms to send and receive packets successfully. Besides, there are other particular problems in WSNs related to the memory and processing. These networks have limited resources because of the cost and size of the devices. The sensors are small in order to be adaptable to all kinds of environments and able to be installed in various conditions, locations and infrastructures. This also causes the batteries to be small and short-lived; thus, herein is the need to save energy in all processes of the network. Due to the wireless conditions, topology dynamics must be taken into account. The time it takes for the network to reconfigure itself will be directly affected by the transmitted and dropped packets. Likewise, the connection and disconnection of nodes alters the packet loss and the rearrangement of the network topology. Here, the routing protocol must provide some rules aimed at reorganizing the links and the topology, and it might also need to establish new routes as default routes. However, these failures have to be only temporary and the protocol must be able to return the network to its stable state in a very short time [2]. Regarding the energy problem, there are specific factors that directly affect node battery consumption. The term unbalanced energy depletion, shown in [3], describes a situation where the nodes that are closer to the coordinator node carry more traffic, and so, they consume more energy than those nodes further away from the root node. This imbalance causes the overall energy consumption to be distributed non-uniformly in the network, making some nodes run out of energy faster than others. A fundamental aspect of node energy consumption is the coverage radio, because it influences the amount of neighbors that a node has and its capacity to forward packets. This coverage should, ideally, reach several strategic points in the network to send information, but it should not affect overhead and energy costs. [PERSON] _et al._ apply probabilistic methods to find the ideal coverage of distributed nodesalong the network. They evaluate the network energy performance based on the lifetime of the sensors and the balance of the energy among them, achieving strategic point location of sensors [4]. Likewise, the work in [5] discusses a method to find the ideal radius considering the average number of neighbors that a node must have in order to forward traffic to the coordinator node without creating overhead and higher energy consumption in the network. Another issue that influences battery consumption is the hop count from source to destination. If the routing protocol finds the shortest routes, then the energy consumption to carry a packet from a source to its destination will be reduced. This is where protocols, such as AODV [6] and DSR [7] optimize energy depletion by choosing the best routes, _i.e._, routes with a lesser hop count. Some authors describe these matters in [8; 9; 10].