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Continuous K-nearest neighbor (CKNN) query is an important type of spatio-temporal queries. Given a time interval [ts, te] and a moving query object q, a CKNN query is to find the K-nearest neighbors (KNNs) of q at each time instant within [ts, te]. In this paper, we focus on the issue of scalable processing of CKNN queries over moving objects with uncertain velocity. Due to the large amount of CKNN queries needed to be evaluated concurrently, efficiently processing such queries inevitably becomes more complicated. We propose an index structure, namely the CI-tree, to predetermine and organize the candidates for each query issued by the user from anywhere and anytime. When the CKNN queries are evaluated, their corresponding candidates can be rapidly retrieved by traversing the CI-tree so that the processing time is greatly reduced. Several experiments are performed to demonstrate the effectiveness and the efficiency of the CI-tree.