An Asynchronous Self-stabilizing Approximation for the Minimum Connected Dominating Set with Safe Convergence in Unit Disk Graphs

Abstract

AbstractIn wireless ad hoc or sensor networks, a connected dominating set (CDS) is useful as the virtual backbone because there is no fixed infrastructure or centralized management. Safe converging self-stabilization is one extension of self-stabilization, that is, self-stabilization guarantees the system tolerates any kind and any finite number of transient faults and doesn’t need any initialization. The safe convergence property guarantees that the system quickly converges to a safe configuration, and then, the system configuration becomes to an optimal configuration without breaking safety. However, the previous works on safe converging algorithm for the minimum CDS assumed a phase clock synchronizer, this 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 the networks modeled by unit disk graphs. The first convergence time to a safe configuration in which a dominating set is computed is 1 round, and the second convergence time to an optimal configuration in which an approximation of the minimum CDS is constructed is O( max {d 2,n}) rounds, O(n 6) steps.KeywordsConvergence TimeSafety PropertyTransient FaultUnit Disk GraphVirtual BackboneThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.