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In this paper, we explore the feature of sharing partial results of multiple queries to reduce the total number of messages incurred. Those queries sharing their partial results are referred to as backbones. Given a set of queries, we shall determine backbones with the purpose of minimizing the total number of messages. Specifically, given a set of queries, we derive a graph, where each vertex represents one query and the corresponding weight edge denotes the number of messages reduced by sharing partial results. Then, we develop a heuristic algorithm SB (standing for Selecting Backbones) to derive a cut in which both backbones and non-backbones are determined. Simulation results show that by sharing partial results, algorithm SB is able to significantly reduce the total number of messages involved.