Minimals Transversals in hypergraphic Wireless Sensor Network

Abstract

Such as background, Wireless sensors networks have become a very widespread domain in the research field along with their representation. The latter has become an important matter to reduce the energy’s consumption as well as to expand the longevity. Thereby, the appearance of a new concept of ”Hyper-graphs” in the last decades has paved the path for studies in all topical areas. That is why we are interested in this new axis. The objective is precisely to determine the connectivity nodes in a network (the nodes play a very important role and ensure the continuity of the information and thus the longevity of the network). Mainly that the major present studies, are the surveillance of wireless sensors networks after deployment. The principle of our method, is that the network of wireless sensors is presented in the form of a ”Voronoi diagram” in order to reduce the complexity of the network through an optimal placement of the nodes. These nodes will be transformed to a hyper-graph through the generation of vertices and hyper-edges where each hyper-edge represents a collection metric. Basing on the properties of hyper-graphs. The second point of our method is that, we shed light on the minimal transversals in order to manage the vertex-cover and on the extraction of connectivity nodes in order to maintain the communication within the wireless sensor network (WSN). In addition, as the WSN could be a dense network, we will disclose the notion of hypergraphic decomposition in order to obtain the best results for the extraction problems that are caused by this kind of graphs (which are known for being difficult and NP-complete problem). As results, We have studied this contribution with some examples and we have proved in this article with an example the importance of the nodes extracted in our network where we have transformed a sensor network to voronoid diagram,then to hypergraph network, decomposition and finaly, the extraction of transversals nodes. Therefore, as conclusion the determination of this nodes have a considerable place in the network, there play the role of ”the connectivity nodes” and its allowed to lengthen network longivity and to guarantee expend the communication.