Improved Algorithms for Fully Dynamic Maximal Independent Set
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Maintaining maximal independent set in dynamic graph is a fundamental open problem in graph theory and the first sublinear time deterministic algorithm was 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 this paper. We present a new simple deterministic algorithm with O(m^2/3√( m)) amortized update time, which improves the previous best result. And we also present the first randomized algorithm with expected O(√(m)^1.5m) amortized time against an oblivious adversary.
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