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Driven by the large-scale growth of applications deployment in data centers and complicated interactions between service components, automated application dependency discovery becomes essential to daily system management and operation. In this paper, we present ADD, which extracts dependency paths for each application by decomposing the application-layer connectivity graph inferred from passive network monitoring data. ADD utilizes a series of statistical techniques and is based on the combination of global observation of application traffic matrix in the data center and local observation of traffic volumes at small time scales on each server. Compared to existing approaches, ADD is especially effective in the presence of overlapping and multi-hop applications and resilient to data loss and estimation errors.