The first generalization concerns the detection model. Indeed, most of works regarding WSN deployment assume a binary detection model. In this paper, a sensor is supposed to surely detect (detection probability is equal to 1) an event if and only if the distance between the sensor and the event is less than a particular sensing range. This model was mainly considered in works addressing area coverage problems, such as target detection or k-coverage problem [2]. The binary model intends to simplify the problem formulation and resolution. Unfortunately, it is not realistic, since the detection of an event depends on multiples factors, including: the distance between the sources and the sensor, the propagation signal attenuation and the accuracy of the sensing level.

We believe that a distance-based probabilistic detection model, including the sensor��s technology and the event characteristics would be more realistic.The second assumption, which was generally considered in the published papers, deals with the fact that the sensing requirement is uniformly distributed within the area. In other words, all the points of the area under monotoring are considered with the same importance. We believe that this assumption does not hold in many environments. Indeed, in many sensor network applications (such as fire detection alarms, water quality monitoring, etc.), the supervised area can request different detection levels, depending on the event��s location. For example, in the case of a fire detection system, high detection probabilities (close to 1) can be required for risky areas (example, those close to chemical deposits or to habitats).

However, for low fire risky places a relative low detection probabilities are sufficient.The third assumption consists on the wireless sensor communication range. Indeed, some existing works suppose that the communication range is very large. Consequently once the sensors are deployed, the resulting wireless communication network graph is supposed to be connected. Clearly, this assumption is not realistic in WSN. Besides, very large transmission range is not adapted in WSN as it implies a great Dacomitinib energy consumption. As a matter of fact, in order to maximize the network lifetime, many works [3] propose solutions which aim to reduce the wireless sensor communication range. In our case study, we assume a reasonable fixed wireless sensor communication range, noted Rc. Our new proposal aims to guarantee the wireless communication network connectivity. To satisfy this new constraint, our proposed method must achieve that the maximum distance separating a sensor with one of its neighbors must be less than Rc.