An Updated Self-stabilizing Algorithm to Maximal 2-packing and A Linear Variation under Synchronous Daemon

In this paper, we first propose an ID-based, constant space, self-stabilizing algorithm that stabilizes to a maximal 2-packing in an arbitrary graph. Using a graph G = (V,E) to represent the network, a subset S ⊆ V is a 2-packing if ∀i ∈ V : |N [i] ∩ S| ≤ 1. Self-stabilization is a paradigm such that each node has a local view of the system, in a finite amount of time the system converges to a global setup with desired property. We argue that the algorithm stabilizes in O(mn) moves under any scheduler (such as a distributed daemon). Secondly, we show that the algorithm stabilizes in O(n) rounds under a synchronous daemon where every privileged node moves at each round. Thirdly, we propose a variation of the algorithm incorporating a local clock counter on each node. We show that it stabilizes in O(n) rounds under a synchronous daemon.