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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 Pˇatra¸scu and Demaine. The new structure(More)
Notations Notations in this lecture are pretty convoluted. In general, quantities withˆ· indicates the empirical version of the corresponding quantity withoutˆ·. Given a loss function , R denote the expected loss under a certain distribution. For example, for 0-1 loss z, R z is the expected 0-1 loss whilê R z is the empirical loss with n i.i.d. samples.(More)
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