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.

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.