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The goal of this paper is to infer the signaling pathway related to lung cancer using Reverse Phase Protein Microarray (RPPM), which provides information on post-translational phosphorylation events. The computational inferring of pathways is obtained by performing Bayesian network in combination with prior knowledge from Protein-Protein Interaction (PPI). A clustering based Linear Programming Relaxation is developed for the searching of optimal networks. The PPI prior knowledge is incorporated into a new scoring function definition based on minimum description length (MDL). In the experiment, we first evaluate the algorithm performance with synthetic networks and associated data. Then we show our signaling network inference for lung cancer using RPPM data. Through the study, we expect to derive new signalling pathways and insight on protein regulatory relationships, which are yet to be known for lung cancer study.