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Auction-based service provisioning and resource allocation have demonstrated strong potential in Cloud-RAN wireless network architecture and heterogeneous networks for effective resource sharing. One major technical challenge is the integration of interference constraints in auction-based solutions. In this work we transform the interference constraint requirement into a set of linear constraints on each cluster. We tackle the generally NP-hard clustering problem by developing a novel practical suboptimal solution that can meet our design requirement. Our novel algorithm utilizes the properties of chordal graphs and applies Lexicographic Breadth First Search (Lex-BFS) algorithm for cluster splitting. This polynomial time approximate algorithm searches for maximal cliques in a graph by generating strong performance in terms of subgraph density and probability of optimal clustering without suffering from the high complexity of the optimal solution.