Self-Stabilizing Small k-Dominating Sets

A self-stabilizing algorithm, after transient faults hit the system and place it in some arbitrary global state, recovers in finite time without external (e.g., human) intervention. In this paper, we propose a distributed asynchronous silent self-stabilizing algorithm for finding a minimal k-dominating set of at most [n/(k+1)] processes in an arbitrary identified network of size n. We propose a transformer that allows our algorithm work under an unfair daemon (the weakest scheduling assumption). The complexity of our solution is in O(n) rounds and O(Dn²) steps using O(log n + k log n/k) bits per process where D is the diameter of the network.