# Cooperative Caching and Resource Allocation in Integrated Satellite-Terrestrial Networks
## 4 Problem Formulation
### Cooperative Caching and Resource Allocation Problem
#### 4.1.4 Problem Description
\tag{17}\]  
where \(\tau_{v}\) is indicated as  
\[\tau_{v}=x_{u,w}\cdot(\sum_{e\in E_{v}^{\text{in}}}a_{u,e}^{w}-\sum_{e\in E_{ v}^{\text{in}}}a_{u,e}^{w}). \tag{18}\]  
As in the above discussion, the joint optimization problem of cooperative caching and resource allocation with multiple physical constraints in (11)-(17) can be given as  
\[\begin{split} min&\phi_{U},\\ s.t.&\eqref{eq:c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_cc_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_cc_c_c_c_cc_c_c_c_cc_c_c_c_c_c_cc_c_c_c_c_c_c_c_c_cc_c_c_c_cc_c_c_c_c_c_c_c_c_c_cc_c_c_c_c_c_c_c_c_c_c_c_cc_c_c_c_c_cc_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_c_cc_c_c_c_c_c_c_c_c_c_c_c_Specifically, for the content service of each user, a neighborhood search approach is used to obtain the feasible strategy of content placement and routing path by traversing both satellites and links in the neighboring sub-network. The access satellite for each user is viewed as the only root candidate in the initial layer, where the root candidate will be firstly searched to obtain a feasible strategy under multiple constraints. When the root candidate is searched, the neighboring satellites of the root candidate will be viewed as the new candidates in the next layer. Note that one satellite with the required content in the sub-network may provide the content service for the current user, then the storage resource usage for the content service of the user can be viewed as 0 according to Equation (1). Therefore, in order to obtain the feasible strategy with minimum deployment costs, whether or not a feasible strategy is obtained in the current layer, the new candidates in the next layer will continue to be searched until the current number of hops is equal to \(h_{sub}\) in the sub-network. When there are insufficient storage resources, restricted content services, or the access satellite of cloud center \(dc\) covered in the sub-network, the content services may be provided by the cloud center. Then, \(L\) shortest paths \(P_{u,dc}^{L}\) between the access satellite of user \(u\) and cloud center \(dc\) can be traversed to obtain the feasible routing path in descending order. An example of content service provisioning by the neighborhood search is illustrated in Figure 3. In the beginning, the neighboring sub-networks of satellite \(v_{0}\) for \(h_{sub}=1\) and \(h_{sub}=2\) are established and represented with green and red lines, respectively. Then, a neighborhood search approach is used to obtain the feasible strategy for content service in the neighboring sub-network with \(h_{sub}=2\). Specifically, for one user, the root candidate in the initial layer, i.e., the access satellite \(v_{0}\), is firstly searched, but a feasible strategy of content service cannot be provided due to the insufficient storage resources. Then, the candidates \(\{v_{1},v_{2},v_{3},v_{4}\}\) in the next layer will be traversed and two feasible strategies can be obtained, i.e., _strategy 1_ and _strategy 2_. For _strategy 1_, satellite \(v_{1}\) has sufficient storage resources to deploy the required content and the content can be transmitted by routing path \(v_{1}\to v_{0}\) to the user. That is, the deployment costs can be composed of onboard storage resource usage and network bandwidth consumption.