## 1 Introduction  
Despite their potential application, wireless sensor networks (WSNs) [1, 2, 3] have severe resource restrictions, such as low computational power, reduced bandwidth, and limited energy sources. Some applications are characterized by their emergency to deliver the data (real-time applications), _i.e._, the data gathering has tight deadlines. Examples of these applications include: surveillance systems, biometric sensing, and intrusion detection. These applications have soft real-time characteristics, _i.e._, environment is not controllable, applications usually use probabilistic models to process data, and communication does not have acknowledgment. By considering the real-time applications in WSNs, we can identify some related work. In general, current contributions consider architectures and mathematical models for general applications [4, 5, 6]. [PERSON] _et al._[7] propose and evaluate a design strategy to determine minimum deadlines used by a specific stream reduction algorithm in general WSNs applications. However, routing and application-level solutions for specific real-time scenarios have been recently proposed [8, 9, 10]. In WSNs applications, physical variables, such as temperature and luminosity, can be monitored continuously along the network operation. The data set representing these physical variables can be referred to as _data-stream_[11]--or _sensor-stream_, considering the WSNs context. As a consequence of this continuous monitoring, we might have high delays in such a way that real-time deadlines are not met. This motivation led us to propose a strategy to control the amount of data gathered by the network and its associated delay. Before introducing our data-centric strategy, allow us to comment on data-stream related work. The data-stream contributions usually focus either in improving stream algorithms [12, 13, 14, 15] or in applying the data-stream techniques to specific scenarios [16, 17, 18, 19, 20]. However, regarding data-stream solutions used in WSNs, we can identify a few researches that consider WSNs as distributed databases in which some functions (e.g., maximum, minimum and average) can be computed in a distributed fashion [21, 22, 23, 24, 25]. Considering real-time requirements and sensor-stream characteristics, we propose a data-centric strategy capable of reducing the data during data routing. In this case, the routing elements consider some application aspects, such as data type and deadline information. Our strategy considers: (1) a project design of real-time application to obtain the minimum deadlines; (2) an analytic model to estimate the ideal sample size used by the reduction algorithms; (3) and two stream-based sampling algorithms to perform data reduction when necessary during the routing task. To validate our data-centric strategy, we use specific scenarios in which application deadlines cannot be met without data reduction. In our simulation, we use a naive tree routing based on shortest-path tree in a flat network. Application information is fed to relay nodes during build and rebuild tree phases. To identify the stream item delay, we consider that the clocks of the nodes are exactly synchronized. Thus, the time synchronization problem in WSNs [26] is not considered here. However, data quality is evaluated to show the associated data reduction impact. Simulation results show that our data-centric strategies meet deadlines without loosing data representativeness. Regarding data reduction strategies for WSNs, current researches use data fusion, aggregation, compression or correlation techniques [3] to help save energy and reduce the packet delay [27, 28, 29]. The closer approach to sample stream reduction is the adaptive sampling, _i.e._, the sampling strategy modifies following the phenomenons variations. The objective of this approach is to improve accuracy, identify correlation and eliminate redundancy [30, 31, 32].