Self-stabilizing algorithm for minimal (α,β)-dominating set

This paper deals with the problem of finding dominating set using self-stabilization paradigm in distributed systems. Usually, members of a dominating set are selected to be as cluster heads in Wireless Sensor Networks (WSN) to ensure a permanent service availability. Since failures occur frequently inside WSN due to limited battery energy, self-stabilizing algorithm allows recomputing the dominating set, and hence the network returns to its ordinary running. Existing works have introduced many variants of self-stabilizing algorithms that compute minimal dominating set S where each node out of S has neighbours in S more than it has out S. In this paper, we introduce a generalized self-stabilizing algorithm called minimal -dominating set. An α-dominating set is a subset of nodes S such that for any node v out of S, the rate of neighbours of v inside S must be greater than α, where . In the same way, an -dominating set is a subset of nodes S such that: S is α-dominating set and for each node v in S, the rate of neighbours of v inside S is greater than β, where . Mathematical proofs and simulation tests show the correctness and the efficiency of the proposed algorithm. Through our proposed variant -domination, we prove rigorously the conjecture of Carrier et al. [Self-stabilizing (f,g)-alliances with safe convergence, J. Parallel Distrib. Comput. 81–82 (2015), pp. 11–23. doi:10.1016/j.jpdc.2015.02.001] who have proposed a self-stabilizing algorithm for a domination variant called -alliance set only when . We prove the correctness of the case f