Event processing applications from financial fraud detection to health care analytics continuously execute event queries with Kleene closure to extract event sequences of arbitrary, statically unknown length, called Complete Event Trends (CETs). Due to common event sub-sequences in CETs, either the responsiveness is delayed by repeated computations or an exorbitant amount of memory is required to store partial results. To overcome these limitations, we define the CET graph to compactly encode

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... l CETs matched by a query. Based on the graph, we define the spectrum of CET detection algorithms from CPU-optimal to memoryoptimal. We find the middle ground between these two extremes by partitioning the graph into time-centric graphlets and caching partial CETs per graphlet to enable effective reuse of these intermediate results. We reveal cost monotonicity properties of the search space of graph partitioning plans. Our CET optimizer leverages these properties to prune significant portions of the search to produce a partitioning plan with minimal CPU costs yet within the given memory limit. Our experimental study demonstrates that our CET detection solution achieves up to 42-fold speedup even under rigid memory constraints compared to the state-of-the-art techniques in diverse scenarios.