-\subsection{ Assumptions and Models}
-\noindent We consider a randomly and uniformly deployed network consisting of
-static wireless sensors. The wireless sensors are deployed in high
-density to ensure initially a high coverage ratio of the interested area. We
-assume that all nodes are homogeneous in terms of communication and
-processing capabilities and heterogeneous in term of energy provision.
-The location information is available to the sensor node either
-through hardware such as embedded GPS or through location discovery
-algorithms. We consider a boolean disk coverage model which is the most
-widely used sensor coverage model in the literature. Each sensor has a
-constant sensing range $R_s$. All space points within a disk centered
-at the sensor with the radius of the sensing range is said to be
-covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$.
-In fact, Zhang and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the
-previous hypothesis, a complete coverage of a convex area implies
-connectivity among the working nodes in the active mode.
-
-\indent Instead of working with the coverage area, we consider for each
-sensor a set of points called primary points~\cite{idrees2014coverage}. We also assume that the
-sensing disk defined by a sensor is covered if all the primary points of
-this sensor are covered.
+
+\subsection{ Assumptions and models}
+
+\noindent We consider a sensor network composed of static nodes distributed
+independently and uniformly at random. A high density deployment ensures a high
+coverage ratio of the interested area at the starting. The nodes are supposed to
+have homogeneous characteristics from a communication and a processing point of
+view, whereas they have heterogeneous energy provisions. Each node has access
+to its location thanks, either to a hardware component (like a GPS unit), or a
+location discovery algorithm.
+
+\indent We consider a boolean disk coverage model which is the most widely used
+sensor coverage model in the literature. Thus, since a sensor has a constant
+sensing range $R_s$, every space points within a disk centered at a sensor with
+the radius of the sensing range is said to be covered by this sensor. We also
+assume that the communication range $R_c \geq 2R_s$. In fact, Zhang and
+Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous
+hypothesis, a complete coverage of a convex area implies connectivity among the
+working nodes in the active mode.
+
+\indent For each sensor we also define a set of points called primary
+points~\cite{idrees2014coverage} to approximate the area coverage it provides,
+rather than working with a continuous coverage. Thus, a sensing disk
+corresponding to a sensor node is covered by its neighboring nodes if all its
+primary points are covered. Obviously, the approximation of coverage is more or
+less accurate according to the number of primary points.
