Sensors_**2009**, \(9\), 7320-7342; doi:10.3390/s90907320  
_Sensors_  
**ISSN 1424-8220**  
www.mdpi.com/journal/sensors  
_Article_  
**Power Conservation through Energy Efficient**  
**Routing in Wireless Sensor Networks**  
**[PERSON] 1,2,*, [PERSON] 1, [PERSON] 2, [PERSON] 2 and [PERSON] 3**  
Footnote 12: footnot  
==WARNING: Truncated because of repetitions==
paths that may me followed. According to SHPER algorithm, each path \(p=(c_{1}\),\(c_{2}\),...,\(c_{n})\) between a lower level cluster head node \(c_{l}\) and the base station \(c_{n}\) that spans \(n-2\) intermediate cluster head nodes \(c_{2}\),...,\(c_{n-1}\), is assigned with a corresponding value of the Routing Index _RI(p)_, which is shown in Equation (1):  
\[RI(p)=\sum_{i=2}^{n-1}Er_{i}-\sum_{i=1}^{n-1}E(c_{i},c_{i+1})\] (1)  
where \(Er_{i}\) denotes the residual energy of the cluster head node \(c_{i}\), and \(E(c_{i}\), \(c_{i+l})\) denotes the energy consumed for a message to be routed between two sequential cluster head nodes \(c_{i}\) and \(c_{i+l}\). If \(A\) is the set of all possible paths \(p_{l}\) that can be followed for the transmission of the messages of a lower level cluster head to the base station, then the path \(p_{k}\) selected is the one which satisfies the property given in Equation (2):  
\[p_{k}=\min\left\{RI(p_{l}):l\in A\right\}\] (2)  
By using Equations (1) and (2) each lower level cluster head defines the mostly energy efficient path to route its messages to the base station and selects the upper level cluster to belong to (step 7). After each node has decided which cluster it belongs to, it informs its corresponding cluster head that is going to be a member of its cluster. Each node transmits this information back to its
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corresponding cluster head using a CSMA (Carrier-Sense Multiple Access) MAC protocol (step 8). That is why, cluster head nodes have to keep their receivers on during this specific step. Each cluster head receives in this way all the messages from the nodes that want to be included in its cluster and creates, according to their quantity, a TDMA schedule of corresponding size (step 9). Then each cluster head broadcasts this schedule back to the nodes in its cluster, in order to inform each node when it can transmit (step 10). Next, the data transmission may start. Thus, during its allocated transmission time, each node sends to its cluster head quantitative data concerning the sensed events. In a way similar to that proposed in TEEN hard and soft thresholds are utilized in the SHPER protocol too. Thus, data are transmitted by a node to its cluster head within its corresponding time slot only when the presence of a sensed event is detected. This happens only when this node measures a value of the sensed attribute which is equal or greater than the hard threshold or when this value changes by an amount equal to or greater than the soft threshold. Along with the data concerning the sensed attributes the node transmits the current value of its residual energy. The radio of each non cluster head node can be turned off until the node's allocated transmission time comes, thus minimizing energy dissipation in these nodes (step 11). Each cluster head collects the data transmitted to it by the nodes of its own cluster (step 12). When all the data have been received, each cluster head performs signal processing functions to aggregate the data it has received along with its own data into a single composite message. This message contains the ID of the node having the highest residual energy among the cluster nodes, along with the most excessive (e.g., maximum) value of the sensed variable and the id of the node that has sensed it (step 13). After each cluster head has created its aggregate message, it waits until its own time slot in order to transmit this aggregate message to the base station either directly, if this is possible, or via intermediate upper level cluster heads according to the path suggested by the use of Equations (1) and (2) (step 14).