Dynamic Distributed MIS with Improved Bounds

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 $O(m^{3/4})$ message complexity, where $m$ denotes the dynamic number of edges in the graph. The algorithm of Assadi et al. is deterministic; to the best of our knowledge, the state-of-the-art distributed algorithm for this problem with a message complexity of $o(m^{3/4})$ incurs a round complexity of $\Omega(m^{1/3})$. We propose a deterministic distributed algorithm that achieves an amortized message complexity of $\tilde{O}(m^{2/3})$ and an amortized round complexity of $\tilde{O}(1)$ under fully dynamic edge updates in the CONGEST model, where $\tilde{O}(\cdot)$ suppresses polylogarithmic factors.