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In this paper, we present BMQ-Processor, a high-performance border-crossing event (BCE) detection framework for large-scale monitoring applications. We first characterize a new query semantics, namely, border monitoring query (BMQ), which is useful for BCE detection in many monitoring applications. It monitors the values of data streams and reports them only when data streams cross the borders of its range. We then propose BMQ-Processor to efficiently handle a large number of BMQs over a high volume of data streams. BMQ-Processor efficiently processes BMQs in a shared and incremental manner. It develops and operates over a novel stateful query index, achieving a high level of scalability over continuous data updates. Also, it utilizes the locality embedded in data streams and greatly accelerates successive BMQ evaluations. We present data structures and algorithms to support 1D as well as multidimensional BMQs. We show that the semantics of border monitoring can be extended toward more advanced ones and build region transition monitoring as a sample case. Lastly, we demonstrate excellent processing performance and low storage cost of BMQ-Processor through extensive analysis and experiments.