Extracting the overlapped sub-regions in wireless sensor networks

In wireless sensor networks, the overlapped sub-regions (faces) are generated due to the intersections among the sensing ranges of nodes. The faces play a significant role in solving the three problems k-coverage (i.e., all the points in the interested field should be covered by at least k active nodes while maintaining connectivity between all active nodes), coverage scheduling and cover sets. To find the faces and discover their coverage degrees, this article presents a distributed algorithm that runs in three steps. First, a colored graph called Intersection Points Colored Graph (IPCG) is proposed, in which the vertices are defined by the range-intersections of nodes-devices and are colored according to the position of these intersections in relation to the ranges of the nodes. The vertex that located on perimeter of the node’s range is colored by red, while the green vertex is an intersection of two ranges inside the range of a third node. The edge that joins two red vertices is colored by red and the edge that joins two green vertices is colored by green while the edge that joins two distinct colored vertices is colored by blue. Second, based on their properties and distinct features, the faces in IPCG are classified into five classes (simple, negative, red, green and positive). Third, based on faces classification, the Three Colored Trees algorithm is proposed to extract the faces in linear time in terms of the number of vertices and edges in IPCG.