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Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms. We present a new randomized dynamic connectivity structure with $O(\log n (\log\log n)^2)$ amortized expected update time and $O(\log n/\log\log\log n)$ query time, which comes within an $O((\log\log n)^2)$ factor of a lower bound due to \Patrascu{} and Demaine. The… (More)

- Mark Heimann, Biaoshuai Tai, Wei Lee, Shang-En Huang
- 2015

Assume we are given the following: • Loss : R → R. Define the risk R (w) = E[(yw, x)]. Note that we said we needed convexity of our loss function last time, but it turns out we don't necessarily need it. We also make the following important assumptions: • ∃ w ∈ W with R (w) = inf v∈W R (v). That is, we assume there exists a minimizer, though this need not… (More)

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