## 2 Related Work
### In-Network Processing (i-NP)  
There is also a history of network processing for _ad-hoc_ networks, specifically for sensor networks, for which energy consumption is one of the most critical problems. One of the alternatives is called in-Network Processing (i-NP), which is to seek energy savings by reducing the number of transmissions.  
The Directed-Diffusion [30] and the LEACH [31] protocols have been proposed to extend the lifetime of energy-constrained wireless sensor networks. Several enhancements to these protocols [32; 33; 34] and also some other approaches were designed with the same idea in mind, such as PER [35], a power-saving hierarchical routing protocol.  
An i-NP approach provides greater efficiency in energy consumption than the traditional centralised server model, in which nodes simply collect and send data to a central powerful node. This i-NP approach seldom considers network issues, for example, the instantaneous load on the network or aspects of the service quality. The intention is to minimise the amount of information before sending it, to minimise the power consumption. Many of the common applications of sensor networks require data processing. The complexity of the process varies significantly from one application to another, even within the same application.  
Download processing has been studied in the context of low-power portable systems. A lower bound on the computation time is derived by [PERSON] _et al._[36]. This bound must be satisfied by any algorithm used by the nodes to communicate and compute, so that the mean square error in the nodes' estimate is within a given interval around zero.  
In wireless sensor networks, one is not interested in downloading all of the data from all of the sensors; instead, there is an interest in simply collecting from a sink node a relevant function of the sensor measurements. An interesting study of the maximum rate at which functions of sensor measurements can be computed and communicated to the sink node is presented by [PERSON] _et al._[37].  
i-NP has been explored by several authors. An approach of aggregation for wireless sensor networks with multiple deposits is proposed by [PERSON] _et al._[38]. The experimental results show a reduction in the number of transmissions and, thus, a savings in energy. In-network processing is also explored by [PERSON] _et al._[39] and describes a protocol for pipelined computation in a structure-free random multihop wireless network. A network-level architecture for distributed sensor systems is presented by [PERSON] _et al._[40], which performs i-NP, whereas heterogeneous nodes are organised in a hierarchical structure dictated by their computational capabilities. The presence of high-performance nodes in the middle of a sea of resource-constrained nodes exposes new commitments for the efficient implementation of applications across the network. Experiments show that, even for a relatively low node density with limited resources compared to high-performance nodes, there are some performance gains for a hierarchical heterogeneous system compared with a homogeneous system. There are some tradeoffs between the run-time implementation, the accuracy of the output produced, and the total energy consumption in the network.