## 2 Routing Protocols in Large-Scale WSNs
### Energy Consumption Mitigation Algorithms  
_ARPES_. [PERSON] _et al._ in [30] proposed an Adaptive Routing Protocol with Energy efficiency and Event clustering for wireless sensor networks (ARPES). The main design features of the proposal are  
Figure 4: Election of relay nodes in OFFIS. energy efficiency, dynamic event clustering, and multi-hop relay considering the trade-off between the residual energy available of the relay nodes and distance from the relay node to the base station. The operation of ARPEES is segmented into rounds, and each round has two stages, _i.e._, forming clusters and selecting cluster heads followed by selecting relay nodes and data transmission. In the first stage, all the nodes are in a sleep state to save battery power in the beginning. When an event is detected in the network, nodes near the event become activated and start measuring the specific sensed attribute. If the sensed attribute value is greater than a predefined threshold, those nodes form a cluster and broadcast a REQ_CLUSTER [ _ID_(_i_),_E_\({}_{\infty}\)_(_i_),_I_(_i_) ] message which consists of the node ID, the amount of residual energy and descriptive information of the sensed data about the event to their neighbors. After that the nodes set their timer for \(t_{I}\). During the period time \(t_{I}\), each nodes within the cluster executes the Cluster Head function as follows:  
\[ \begin{array}{l}F_{CH}\left(i\right)=E_{res}(i)\times I\left(i\right),\forall i \in X\\ Max\ F_{CH}\left(i\right)-\frac{\forall i\in X}{\mathit{sat}\ \mathit{at}\ \mathit{at}}\end{array}  \tag{1}\]  
This function ensures that the node which is the nearest to the event and with maximum energy available will be selected as the cluster head. The cluster head stores the node ID of all the nodes in this cluster, and creates the TDMA schedule to arrange each node when the nodes can transmit their sensed data to the cluster head. In the second stage, using the TDMA schedule described above, each sensor node transmits the sensed information to its cluster head during their allocated transmission period. According to the TDMA scheme, the node that has more data information will transmit with priority and with more time slots than others. Then data aggregation will be performed at the CH and the total bits of data packets can be reduced accordingly. In the phase of selecting relay nodes and creating a route, the cluster head broadcasts an REQ_RELAY message to all the neighboring nodes. Each node that receives the REQ_RELAY message calculates its residual energy and distance to the base station, and then puts the results into an ACK_RELAY message, and sends the message back to the cluster head. The cluster head waits a period for receiving all the ACK_RELAY messages from relay node candidates and checks whether it can transmit data to the base station directly. The desired relay node should satisfy three conditions: the maximum amount of residual energy, the maximum distance from the cluster head and the minimum distance to the base station, being located on the approximate straight path between cluster head and base station. These conditions can be expressed by the Relay Node function, which is defined as follows:  
\[ \begin{array}{l}F_{\mathit{EN}}\left(j\right)=E_{res}\left(j\right)\times \frac{d\left(CH,j\right)}{d\left(j,BS\right)}\times cos\ \alpha_{j},\forall j\in Y\\ Max\ F_{\mathit{RN}}\left(j\right)-\frac{\forall i\in Y}{\mathit{ overlay}\ \mathit{Relay\ Node}}\\ cos\ \alpha_{j}=\frac{d\left(CH,j\right)^{2}+d\left(CH,BS\right)^{2}-d\left(j,BS \right)^{2}}{2d\left(CH,j\right)d\left(CH,BS\right)}\end{array}  \tag{2}\]  
ARPEES outperforms LEACH thanks to its multi-hop transmission, thus balancing energy consumption over several relay nodes rather than focusing energy consumption on the CH. Besides, it achieves load balance by selecting the node with maximum residual energy as the relay node, and the hot spot problem is alleviated.