Data stream processing and analytics (DSPA) applications are widely used to process the ever increasing amounts of data streams produced by highly geographical distributed data sources such as fixed and mobile IoT devices in order to extract valuable information in a timely manner for real-time actuation. To efficiently handle this ever increasing amount of data streams, the emerging Edge/Fog computing paradigms is used as the middle-tier between the Cloud and the IoT devices to process data streams closer to their sources and to reduce the network resource usage and network delay to reach the Cloud. In this paper, we account for the fact that both network resources and computational resources can be limited and shareable among multiple DSPA applications in the Edge-Fog-Cloud architecture, hence it is necessary to ensure their efficient usage. In this respect, we propose a resource-aware and time-efficient heuristic called SOO that identifies a good DSPA operator placement on the Edge-Fog-Cloud architecture towards optimizing the trade-off between the computational and network resource usage. Via thorough simulation experiments, we show that the solution provided by SOO is very close to the optimal one while the execution time is considerably reduced.