Shang-En Huang

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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)) amortized expected update time and O(log n/ log log log n) query time, which comes within an O((log log n)) factor of a lower bound due to Pǎtraşcu and Demaine. The new structure is(More)
A (β, )-hopset is, informally, a weighted edge set that, when added to a graph, allows one to get from point a to point b using a path with at most β edges (“hops”) and length (1 + ) dist(a, b). In this paper we observe that Thorup and Zwick’s sublinear additive emulators are also actually (O(k/ ), )hopsets for every > 0, and that with a small change to the(More)
Notations Notations in this lecture are pretty convoluted. In general, quantities with ·̂ indicates the empirical version of the corresponding quantity without ·̂. Given a loss function `, R` denote the expected loss under a certain distribution. For example, for 0-1 loss z, Rz is the expected 0-1 loss while R̂z is the empirical loss with n i.i.d. samples.(More)
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