An asynchronous self-stabilizing approximation for the minimum CDS with safe convergence in UDGs

A connected dominating set (CDS) is useful in forming a virtual backbone in wireless ad hoc or sensor networks because these networks lack a fixed infrastructure and centralized management. Self-stabilization guarantees that the system tolerates any finite number of transient faults and does not need any initialization. The safe convergence property guarantees that the system quickly converges to a feasible safe configuration, and subsequently converges to a legitimate configuration without violating safety. A previous publication on a safely converging algorithm for the minimum CDS assumed a phase clock synchronizer, which is a very strong assumption. In this paper, we propose the first asynchronous self-stabilizing (6+ϵ)-approximation algorithm with safe convergence for the minimum CDS in networks modeled by unit disk graphs (UDGs). We assume that the feasible safe configuration satisfies the condition that a dominating set is constructed. The convergence time to a feasible safe configuration is one round, and the convergence time to a legitimate configuration in which an approximated minimum CDS is constructed is O(max⁡{d2,n}) rounds, and O(n6) steps.