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Maintaining maximal independent set in dynamic graph is a fundamental openproblem in graph theory and the first sublinear time deterministic algorithmwas came up by Assadi, Onak, Schieber and Solomon(STOC'18), which achieves$O(m^{3/4})$ amortized update time. We have two main contributions in thispaper. We present a new simple deterministic algorithm with$O(m^{2/3}\sqrt{\log m})$ amortized update time, which improves the previousbest result. And we also present the first randomized algorithm with expected$O(\sqrt{m}\log^{1.5}m)$ amortized time against an oblivious adversary.

Improved Algorithms for Fully Dynamic Maximal Independent Set