Before revision: The problem of maintaining a maximal independent set (MIS) in a dynamic graph has received growing attention in recent years. In STOC'18, Assadi et al. presented a distributed algorithm for maintaining an MIS with O(1) ( amortized) round complexity and O(m^{3/4\left(\log^2 n}\right) \left(\right)  ]  Assadi et al. is deterministic;
After revision: The field of dynamic graph algorithms aims at achieving a thorough understanding of real-world networks whose topology evolves with time. Traditionally, the focus has been on the classic sequential, centralized setting where the main quality measure of an algorithm is its update time, i.e. the time needed to restore the solution after each update. While real-life networks are very often distributed across multiple machines, the fundamental question of finding efficient dynamic, distributed graph algorithms received little attention to date. The goal in this setting is to optimize both the round and message complexities incurred per update step, ideally achieving a message complexity that matches the centralized update time in O(1) ( amortized) round complexity and O(m^{3/4\left(\log^2 n}\right) \left(\right) ] Assadi et al. is deterministic;