A Perturbation-Proof Self-stabilizing Algorithm for Constructing Virtual Backbones in Wireless Ad-Hoc Networks

Abstract

Self-stabilization is a key property of fault-tolerant distributed computing systems. A self-stabilizing algorithm ensures that the system eventually converges to a legitimate configuration from arbitrary initializations without any external intervention, and it remains in that legitimate configuration as long as no transient fault occurs. In this paper, the problem of virtual backbone construction in wireless ad-hoc networks is first translated into its graph-theoretic counterpart, i.e., approximate minimum connected dominating set construction. We then propose a self-stabilizing algorithm with time complexity O(n). Our algorithm features a perturbation-proof property in the sense that the steady state of the system gives rise to a Nash equilibrium, effectively discouraging the selfish nodes from perturbing the legitimate configuration by changing their valid states. Other advantages of this algorithm include increasing accessibility, reducing the number of update messages during convergence, and stabilizing with minimum changes in the topological structure. Proofs are given for the self-stabilization and perturbation-proofness of the proposed algorithm. The simulation results show that our algorithm outperforms comparable schemes in terms of stabilization time and number of state transitions.