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Smartphones are nowadays equipped with a number of sensors, such as WiFi, GPS, accelerometers, etc. This capability allows smartphone users to easily engage in crowdsourced computing services, which contribute to the solution of complex problems in a distributed manner. In this work, we leverage such a computing paradigm to solve efficiently the following problem: comparing a query trace Q against a crowd of traces generated and stored on distributed smartphones. Our proposed framework, coined SmartTrace+, provides an effective solution without disclosing any part of the crowd traces to the query processor. SmartTrace+, relies on an in-situ data storage model and intelligent top-K query processing algorithms that exploit distributed trajectory similarity measures, resilient to spatial and temporal noise, in order to derive the most relevant answers to Q. We evaluate our algorithms on both synthetic and real workloads. We describe our prototype system developed on the Android OS. The solution is deployed over our own SmartLab testbed of 25 smartphones. Our study reveals that computations over SmartTrace+ result in substantial energy conservation; in addition, results can be computed faster than competitive approaches. [ABSTRACT FROM PUBLISHER]