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In this paper, we introduce the notion of sufficient set and necessary set for distributed processing of probabilistic top-k queries in cluster-based wireless sensor networks. These two concepts have very nice properties that can facilitate localized data pruning in clusters. Accordingly, we develop a suite of algorithms, namely, sufficient set-based (SSB), necessary set-based (NSB), and boundary-based (BB), for intercluster query processing with bounded rounds of communications. Moreover, in responding to dynamic changes of data distribution in the network, we develop an adaptive algorithm that dynamically switches among the three proposed algorithms to minimize the transmission cost. We show the applicability of sufficient set and necessary set to wireless sensor networks with both two-tier hierarchical and tree-structured network topologies. Experimental results show that the proposed algorithms reduce data transmissions significantly and incur only small constant rounds of data communications. The experimental results also demonstrate the superiority of the adaptive algorithm, which achieves a near-optimal performance under various conditions.