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- Shang-En Huang, Dawei Huang, Tsvi Kopelowitz, Seth Pettie
- SODA
- 2017

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)

- Shang-En Huang, Seth Pettie
- ArXiv
- 2017

A $(\beta,\epsilon)$-$\textit{hopset}$ 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 $\beta$ edges ("hops") and length $(1+\epsilon)\mathrm{dist}(a,b)$. In this paper we observe that Thorup and Zwick's $\textit{sublinear additive}$ emulators are also actually… (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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