# SIoT: A New Strategy to Improve the Network Lifetime with an Efficient Search Process
## 3 Preliminaries
### Problem Definition  
In a constraint network, each node has a set of neighbors, where the communication is one hop (from a node to another), in both directions (undirected network), and is unicast (a request is sent to just one node).  
In a social network, each node has a set of friends which are considered useful neighbors to reach the requested services. So, the problem consists of how to select these friends in a way that can improve network navigability. Furthermore, the search process must be rapid with an increased network lifetime.  
In more details, when any network does not achieve the total giant component (100%), the possibility to respond to the users' or nodes' requirements will be decreased. The average degree should be minimized considering that the total giant component should be maximized, where a high number of friends affect the nodes' capabilities such as power energy and memory capacity. Moreover, the minimization of average path length and diameter, and the maximization of the average local coefficient boost the service search to find a short path from a requestor to a provider. Besides, until the provider node is not achieved, the request/queries should move through the nodes that have high capabilities, especially the ones with sufficient energy. This is because intermediate nodes with insufficient resources could break down after several tasks.  
Figure 2 shows a simple example of a social network (it is considered as a mesh-like network), where links represent friendships' connection ties, while the dashed lines are the path followed by node S to reach the provider node D. When a node S receives a request, it can retransmit or execute it; in case of retransmission, the node S can choose the friend A, and by the same manner, the request will reach to the provider (executor) node D. The path achieved by the request in this example is the shortest path length; it makes the service search rapid, but that does not mean that it is the best path. Node A can transmit the requests more frequently than others; therefore, it will consume more energy. For this, during the search phase, the best path to achieve a provider is a short path (for the rapid search phase), where the associated/constructed nodes have sufficient energies (to extend the network lifetime [34]).  
Table 2 summarizes the main notations used in the rest of this paper.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Network** & **Service** & **Energy** & **Network** \\  & **Navigability** & **Search** & **Consumption** & **Lifetime** \\ \hline [PERSON] et al. [24] (2014) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) \\ [PERSON] et al. [25] (2018) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) \\ [PERSON] et al. [26] (2019) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) \\ [PERSON] et al. [27] (2019) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) \\ [PERSON] et al. [28] (2015) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) \\ [PERSON] et al. [29] (2016) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) \\ [PERSON] et al. [30] (2017) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) \\ [PERSON] et al. [33] (2020) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) \\ Our proposal & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Functional comparison of our proposal work with the previous studies.