Fully Dynamic Maximal Independent Set in Expected Poly-Log Update Time

09/08/2019 ∙ by Shiri Chechik, et al. ∙ 0

In the fully dynamic maximal independent set (MIS) problem our goal is to maintain an MIS in a given graph G while edges are inserted and deleted from the graph. The first non-trivial algorithm for this problem was presented by Assadi, Onak, Schieber, and Solomon [STOC 2018] who obtained a deterministic fully dynamic MIS with O(m^3/4) update time. Later, this was independently improved by Du and Zhang and by Gupta and Khan [arXiv 2018] to Õ(m^2/3) update time. Du and Zhang [arXiv 2018] also presented a randomized algorithm against an oblivious adversary with Õ(√(m)) update time. The current state of art is by Assadi, Onak, Schieber, and Solomon [SODA 2019] who obtained randomized algorithms against oblivious adversary with Õ(√(n)) and Õ(m^1/3) update times. In this paper, we propose a dynamic randomized algorithm against oblivious adversary with expected worst-case update time of O(log^4n). As a direct corollary, one can apply the black-box reduction from a recent work by Bernstein, Forster, and Henzinger [SODA 2019] to achieve O(log^6n) worst-case update time with high probability. This is the first dynamic MIS algorithm with very fast update time of poly-log.

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