Introducing the Self-Stabilizing SLEEPING Model

Abstract

The SLEEPING LOCAL model introduces a new complexity parameter, the awake complexity, to make distributed algorithms energy-efficient. In the synchronous LOCAL model, nodes can now decide to be awake or asleep in each round. In a round, only awake nodes can communicate to share information, which consumes energy. The awake complexity is the maximum number of times a node is activated to produce an output. In particular, it often comes at the cost of the total number of rounds required to solve a problem, compared with algorithms in which every node is awake in every round. In this article, we adapt the notion of awaken rounds to the context of self-stabilization, introducing the Self-Stabilizing SLEEPING model. Nodes are no longer required to remain awake at all times. However, in self-stabilization, nodes must be activated infinitely often to detect any issue in the system's current state. In this model, the complexities are: * How many synchronous rounds are needed to reach a legitimate configuration? * How many times does a node need to be awake to reach this configuration? * How often does a node need to be awake once this configuration is reached? The goal is to minimize those three metrics, and we can expect different trade-offs. We present energy-efficient algorithms to solve the problems of finding a $(\Delta+1)$-coloring, a Maximal Independent Set, and a Maximal Matching, thanks to new ad hoc sleeping techniques that reduce the awake complexity (i.e., energy consumption) during the convergence phase. We also propose two transformers that adapt silent self-stabilizing algorithms to the SLEEPING setup. The first transformer is pretty simple and deals with low-complexity algorithms. The second is more elaborate and is more energy-efficient when it transforms slow self-stabilizing algorithms.