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.
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