Small Worlds in the Tree Topologies of Wireless Sensor Networks

In this study, the characteristics of small worlds are investigated in the context of the tree topologies of wireless sensor networks. Tree topologies, which construct spatial graphs with larger characteristic path lengths than random graphs and small clustering coefficients, are ubiquitous in wireless sensor networks. Suffering from the link rewiring or the link addition, the characteristic path length of the tree topology reduces rapidly and the clustering coefficient increases greatly. The variety of characteristic path length influences the time synchronization characteristics of wireless sensor networks greatly. With the increase of the link rewiring or the link addition probability, the time synchronization error decreases drastically. Two novel protocols named LEACH-SW and TREEPSI-SW are proposed to improve the performances of the sensor networks, in which the small world characteristics are taken into use to reduce the time synchronization errors.