## 3 An Opportunistic Routing for Data Forwarding Based on Vehicle Mobility Association
### Definition and Analysis  
In most of the routing algorithms, the replica information is a type of routing overhead. OVMA preserves replica information and primarily records the degree of association between vehicles and the path of message passing. OVMA is designed as a two-phase algorithm:  
* Information efficient region boundary phase. The replica information (exchange information, EM; response information, HM) and parameters definition are shown in Table 1:  
* EM (Ev, Es, Ec, Er, \(tabu_{n}\), Ert) represents exchange information, which means that the replica information is carried and can spread in a certain range. * HM (Request) refers to the response information, which contains the response information and can spread in a certain range. Suppose that the vehicles and the paths between vehicles can be abstracted into a graph theory problem of points and lines. The distance between vehicles can be acquired by GPS, and each vehicle carries EM and HM information and spreads in a fixed time. Information efficient region phase: we can define a topological structure Graph G = (V, E), where V is the node in network, E is edge which can show as E = \(\{e_{ij}\mid i\in\text{V},j\in\text{V}\}\), and \(i\) and \(j\) are nodes. \(d_{ij}\) is weighted between \(i\) and \(j\). We assume that the process of forwarding information about the network is always propagated along the optimal path and the propagation of information between the two nodes always first looks for the nearest node as the next hop information transmission node. The network information transfer rate from the \(i\) node and the \(j\) node: \(\alpha_{t}[d_{ij}(t)]\). This can be expressed as the reciprocal of the weight of the \(i\) node and the \(j\) node. \[\alpha_{t}[d_{ij}(t)]=\frac{1}{d_{ij}(t)} \tag{1}\]  
Therefore, the efficiency of the whole network G: \(\alpha_{t}[\text{G}]\) can be defined as the average of the information transmission efficiency of each node, and there are \(n\) nodes in the network. \[\alpha_{t}[G]=\frac{1}{n(n-1)}\sum_{i\
eq j\in G}\frac{1}{d_{ij}} \tag{2}\]  
In vehicular networks, if a node is directly associated with many other nodes, the node is in the central position within the network. The degree of association between nodes is utilized to intuitively represent the role of nodes in the network. The influence of the association degree on the overall transmission efficiency of the network can be calculated by calculating the information centrality of the edges connected between nodes. \(\xi_{ij}(t)\) is the information centrality of the edge \(e_{ij}\), which is defined as the relative reduction in the transmission efficiency of the entire network when the edge \(e_{ij}\) is removed. \[\xi_{ij}=\frac{\alpha_{t}[G]-\alpha_{t}[d_{ij}(t)]}{\alpha_{t}[G]} \tag{3}\]  
Accordingly, the association degree between nodes function is formulated as Equation (4). \[\delta_{ij}(t)=1-\xi_{ij}(t) \tag{4}\]  
Supposing \(v_{i}(t)\) and \(v_{j}(t)\) are two arbitrary points at time \(t\), \(\gamma\) represents the frequent set of nodes with \(i\) node that the degree of association greater than \(\mu\) (\(\delta_{ij}(t)>\mu\)) at moment \(t\). \(\delta_{ij}(t)\) represents the degree of association among nodes. \(\gamma\) can be expressed as:  
\[\gamma=\{\delta_{ij}(t)>\mu|v_{i},v_{j}\in V\} \tag{5}\]  
At the initial time, each node has the same degree of association that recorded in Ec, \(\delta_{ij}(t)\) = Q. The optimal solution of the data delivery can be achieved by the directed graph \(g=(v,e,\gamma)\).