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A continuous nearest neighbor (CNN) search, which retrieves the nearest neighbors corresponding to every point in a given query line segment, is important for location-based services such as vehicular navigation and tourist guides. It is infeasible to answer a CNN search by issuing a traditional nearest neighbor query at every point of the line segment due to the large number of queries generated and the overhead on bandwidth. Algorithms have been proposed recently to support CNN search in the traditional client- server systems but not in the environment of wireless data broadcast, where uplink communication channels from mobile devices to the server are not available. In this paper, we develop a generalized search algorithm for continuous k-nearest neighbors based on Hilbert Curve Index in wireless data broadcast systems. A performance evaluation is conducted to compare the proposed search algorithms with an algorithm based on R-tree Air Index. The result shows that the Hilbert Curve Index-based algorithm is more energy efficient than the R-tree-based algorithm.