Self‐Stabilizing Algorithms for the Dynamic Total Domination Problem

ABSTRACT In a network , a set of processes is a total dominating set if and only if every process is neighboring to some member of . We introduce the dynamic total domination problem , a novel synchronization challenge that requires sustaining a total dominating set in a network over time. Unlike static approaches, this problem ensures that every process always has at least one neighbor in , while processes alternate between entering and exiting . This problem has practical applications, notably in environmental monitoring IoT systems powered by rechargeable batteries, where continuous sensing coverage is essential. In this paper, we propose two self‐stabilizing distributed algorithms for the dynamic total domination problem under a weakly fair distributed scheduler. The first algorithm utilizes unbounded timestamps, while the second employs bounded timestamps. Both algorithms guarantee convergence in rounds and ensure safety and liveness without centralized control. In the synchronized model (a special case of distributed scheduler), the waiting times of both algorithms are rounds.