## 3 Cluster-Disjoint Multipath Routing Protocol
### Grid Cluster Construction
In addition, since it relays efficiency to the neighboring grid cluster, the location of the node is considered to be the second factor. The equation for calculating the priority \(P\) for the cluster head considering remaining energy \(E_{remaining}\), total energy amount \(E_{total}\), and distance from center of each grid cluster \(D_{cton}\) is as follows:

\[P=E_{remaining}/E_{total}*\alpha+\frac{D_{cton}}{R}*\beta\]

In the above equation, \(\alpha\) and \(\beta\) are user-defined variables, respectively. They could be used arbitrarily to assign importance to each factor according to the requirements of the user or applications. In Figure 2, the priority of each node is as follows, in the bold grid (in this case, it is assumed that the total energy \(E_{total}\) is 1000 and the transmission radius \(R\) is 50 m). Assuming that the lower the \(P\) value, the higher the priority, it is in the order of Node 4 (\(P\) = 1.3), Node 2 (\(P\) = 1.5), Node 5 (\(P\) = 1.7), Node 3 (\(P\) = 2), Node 1 (\(P\) = 2.2), and Node 6 (\(P\) = 2.2). Nodes 1, 3, and 6, which have high remaining energy, might seem the most appropriate candidates; however, if the distance from the center of each grid cluster is far, they could not be appropriate as candidates. For example, if Node 3 is selected as the cluster head, Node 5 would be waste that has to be delivered to Node 3 via Node 4 to transmit the packet to the neighboring grid cluster. ### Cluster-Disjoint Multipath Packet Transmission

In this section, we describe a process of transmitting a packet through a multipath based on the grid cluster. The packet transmission process consists of the following three phases. * In the first phase, the source node which detected the event delegates the packet to the cluster head of its grid cluster. * The cluster head calculates the required number of paths based on the requirement of application or the user in the second phase. * Finally, the cluster head branches by the required number of paths and transmits the packet. The source node which detected the event delegates the packet to the cluster head of the grid cluster to which it is assigned. The cluster head which is entrusted with the packet transmission calculates the required number of paths to satisfy the needs (e.g., end-to-end transmission success ratio) of application or the user. The required number of paths is calculated based on the single hop transmission success ratio and a required end-to-end transmission success ratio [11]. After calculating the required number of paths, the cluster head exploits the grid clusters located on the straight line to the grid cluster where the sink is located as a first path. The other paths are composed of grid clusters surrounding the first path. Figure 3 shows the data transmission process exploiting the cluster-disjoint multipath. As described above, the source node which detects the event delegates the packet to the cluster head of grid cluster C(0, 3) to which it belongs. The cluster head calculates a straight line to grid cluster C(3, 0) where the sink node is located in order to construct the first path (the black dot line in Figure 3. The cluster head could find out which grid cluster to pass through to transmit the packet to the sink node. In Figure 3, the black dot line penetrates the grid cluster represented in gray, and these grid clusters can become the first path. However, in the case where data can be sent from grid cluster C(0, 3) to grid cluster C(1, 2) located at the diagonal without passing through cluster C (1, 3), although a black dot line penetrates the grid cluster, it does not exploit it as part of first path. To deal with a case of more paths required according to the requirement of application or the user, the cluster head which participated in the first path in the process of transmitting the packet informs the neighboring grid cluster that it is participating in the first path.