Sensor networks have promising applications such as battlefield surveillance, biological detection, and emergency navigation, etc. Crucial problems in sensor networks are energy-efficiency and collision avoidance in wireless communication. To deal with the problems, we consider a self-stabilizing solution to the construction of k disjoint sense-sleep trees, where range adjustment and the use of GPS are allowed. Each root is determined by its identifier and is distinguished by its color, the identification of a tree. Using a dominating k-partition rule, each non-root node first determines a color irrelevant to the root. Then, the non-root node determines a parent node that is equally colored with minimal distance. If there is no appropriate parent, the range is extended or shrunk until the nearest parent is determined. Finally, we perform a simulation.

Most conventional studies on self-stabilization have been indifferent to the vulnerability under convergence. This paper investigates how mutual exclusion property can be achieved in self-stabilizing rings even for illegitimate configurations. We present a new method which uses a state with a large state space to detect faults. If some faults are detected, every process is reset and not given a privilege. Even if the reset values are different between processes, our protocol mimics the behavior of Dijkstra's unidirectional K-state protocol. Then we have a fast and safe mutual exclusion protocol. Simulation study also examines its performance.