  In this paper, the cooperative caching problem in fog radio access networks
(F-RAN) is investigated. To maximize the incremental offloaded traffic, we
formulate the clustering optimization problem with the consideration of
cooperative caching and local content popularity, which falls into the scope of
combinatorial programming. % and is NP-hard. We then propose an effective
graph-based approach to solve this challenging problem. Firstly, a node graph
is constructed with its vertex set representing the considered fog access
points (F-APs) and its edge set reflecting the potential cooperations among the
F-APs. %whether the F-APs the distance and load difference among the F-APs.
Then, by exploiting the adjacency table of each vertex of the node graph, we
propose to get the complete subgraphs through indirect searching for the
maximal complete subgraphs for the sake of a reduced searching complexity.
Furthermore, by using the complete subgraphs so obtained, a weighted graph is
constructed. By setting the weights of the vertices of the weighted graph to be
the incremental offloaded traffics of their corresponding complete subgraphs,
the original clustering optimization problem can be transformed into an
equivalent 0-1 integer programming problem. The max-weight independent subset
of the vertex set of the weighted graph, which is equivalent to the objective
cluster sets, can then be readily obtained by solving the above optimization
problem through the greedy algorithm that we propose. Our proposed graph-based
approach has an apparently low complexity in comparison with the brute force
approach which has an exponential complexity. Simulation results show the
remarkable improvements in terms of offloading gain by using our proposed
approach.
