Self-stabilizing algorithms of constructing virtual backbone in selfish wireless ad-hoc networks

A self-stabilizing system tolerates any transient faults and does not need any initialization. In wireless ad-hoc networks, a connected dominating set is the graph-theoretic counterpart of a virtual backbone. In this paper, we propose two distributed self-stabilizing algorithms for approximate minimum connected dominating set construction with perturbation-proof property in the sense that the legitimate configuration of the system gives rise to a Nash equilibrium, effectively discouraging the selfish nodes from perturbing the legitimate configuration by changing their valid states. The legitimate configuration of our first algorithm is always a Nash equilibrium regardless of the specifics of the nodes' utility functions, while the configurations reached in our second algorithm are Nash equilibria only if the selfish nodes explicitly prefer to be out of the virtual backbone. The second algorithm suits in particular for scenarios with multiple legitimate configurations, while the first algorithm always gives rise to a unique configuration. Both algorithms increase accessibility, reduce the number of update messages during convergence, and stabilize with minimum changes in the topological structure. Proofs are given for the self-stabilization and perturbation-proofness of the proposed algorithms. The simulation results show that our two algorithms outperform comparable schemes in terms of stabilization time and the number of state transitions.