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Given a large spatio-temporal database of events, where each event consists of the fields event ID, time, location, and event type, mining spatio-temporal sequential patterns identifies significant event-type sequences. Such spatio-temporal sequential patterns are crucial to the investigation of spatial and temporal evolutions of phenomena in many application domains. Recent research literature has explored the sequential patterns on transaction data and trajectory analysis on moving objects. However, these methods cannot be directly applied to mining sequential patterns from a large number of spatio-temporal events. Two major research challenges still remain: 1) the definition of significance measures for spatio-temporal sequential patterns to avoid spurious ones and 2) the algorithmic design under the significance measures, which may not guarantee the downward closure property. In this paper, we propose a sequence index as the significance measure for spatio-temporal sequential patterns, which is meaningful due to its interpretability using spatial statistics. We propose a novel algorithm called Slicing-STS-miner to tackle the algorithmic design challenge using the spatial sequence index, which does not preserve the downward closure property. We compare the proposed algorithm with a simple algorithm called STS-miner that utilizes the weak monotone property of the sequence index. Performance evaluations using both synthetic and real-world data sets show that the slicing-STS-miner is an order of magnitude faster than STS-Miner for large data sets.