# An Optimization Routing Algorithm for Green Communication in Underground Mines
## 4 Routing Algorithm Based on DCMST  
GCUM functions are used to manage miners who are wearing the mobile node modules, supervise the production schedule under normal conditions, and protect miners in the mine when accidents occur. Reliable connectivity, as established from the DCMST, ensures that nodes in the network are connected, and an optimized network structure can be obtained in which energy consumption is reduced and the network lifetime is extended. Therefore, the routing algorithm based on the DCMST can effectively distinguish among node types. In the context of low power consumption and green communication, the DCMST can identify reliable routing paths and derive the weight equation of each path and the degree of residual energy of each node. Figure 1a shows a diagram of the communication between nodes in tunnels in an underground mine. The numbers that are marked on the lines are the weights of the respective routing paths. The DCMST is introduced to initialize the MST of the network. Each edge in the MST is a routing path between connected nodes that guarantees connectivity and achieves the lowest overhead, as shown in Figure 1b. In this paper, the GCUM is regarded as a simple, connected, and undirected graph, and a DCMST algorithm for heterogeneous nodes is proposed [35]. \(G\) is an undirected complete network; \(V\) is the set of nodes in the GCUM; and \(E\) is the set of edges. Additionally, \(\mathrm{W}=\left(w_{ij}\right)_{n\times n}\) is the weight matrix of G, where \(w_{ij}=w_{ji}\) and \(w_{ii}=+\infty\)\((i,\)\(j=1,2,\ldots,\)\(n)\). If \(v_{i}v_{j}\in E\), then \(w_{ij}=w\big{(}v_{i}v_{j}\big{)}\); otherwise, \(w_{ij}=+\infty\). Moreover, \(h_{i}\)\((i=1,\)\(2,\)\(\ldots,n)\) is defined as the degree of each node in the network. **Definition 1**. : \(G(V,E,W)\) _is defined as an undirected complete network, where \(v_{0}\in V\) is a node of G and y is a positive integer. If \(T\) is a spanning tree of \(G\) and \(d_{t}(v_{0})=y\), \(T\) is the h-degree constraint spanning tree for node \(v_{0}\) in network G._  
**Definition 2**. : \(G(V,E,W)\) _is defined as an undirected complete network, where \(v_{0}\in V\) is a node of G. Among all spanning trees of \(G\), if the degree \(k\) of \(v_{0}\) is maximized and the weights of the edges are minimized in the spanning tree, the tree is defined as the maximum degree constraint MST of node \(v_{0}\) in \(G\)._  
Therefore, the weight of edges can be replaced by \(E_{s}^{T}(\lambda_{2}t,d)\), and searching for the minimum weight of an edge is equivalent to find the minimum \(E_{s}^{T}\) with minimum parameters of throughput \(1-\lambda_{2}\) and distance \(d\). In addition, \(d_{T^{\prime}}(v_{0})\) will be defined as the degree of node \(v_{0}\), which represents the maximum edges that connect with it. In this paper, the degree of the nodes will be constrained to prevent unnecessary energy consumption by multi-path connections. Therefore, according to the residual energy function (Equation (2)),  
Figure 1: (**a**) Diagram of a node communication network in an underground mine. (**b**) Diagram after the DCMST is applied to the node communication network in an underground mine. two thresholds, \(\delta_{0}\) and \(\delta_{1}\) (\(0<\delta_{0}<\delta_{1}<\) initial energy), are set to assign the degree \(h\). The maximum degree of ONs is set to 2. When the residual energy is above \(\delta_{1}\), the maximum degree of ANs and MNs are set as unlimited and six, respectively. When the residual energy is interposed between \(\delta_{0}\) and \(\delta_{1}\), the maximum degree of ANs and MNs are set as six and four, respectively. When the residual energy is below \(\delta_{0}\), the maximum degree of ANs and MNs are both set to two. Constraining the degree of the node effectively controls the multi-path connection problem and effectively extends the network lifetime. Therefore, \(G(V,E,W)\) is defined as an undirected complete network, where \(v_{0}\in V\) is a node of \(G\).