# Zhengyu Wang

## Publications Authored By Zhengyu Wang

In the communication problem $\mathbf{UR}$ (universal relation) [KRW95], Alice and Bob respectively receive $x, y \in\{0,1\}^n$ with the promise that $x\neq y$. The last player to receive a message must output an index $i$ such that $x_i\neq y_i$. We prove that the randomized one-way communication complexity of this problem in the public coin model is exactly $\Theta(\min\{n,\log(1/\delta)\log^2(\frac n{\log(1/\delta)})\})$ for failure probability $\delta$. Read More

In the communication problem $\mathbf{UR}$ (universal relation) [KRW95], Alice and Bob respectively receive $x$ and $y$ in $\{0,1\}^n$ with the promise that $x\neq y$. The last player to receive a message must output an index $i$ such that $x_i\neq y_i$. We prove that the randomized one-way communication complexity of this problem in the public coin model is exactly $\Theta(\min\{n, \log(1/\delta)\log^2(\frac{n}{\log(1/\delta)})\})$ bits for failure probability $\delta$. Read More

The task of finding heavy hitters is one of the best known and well studied problems in the area of data streams. In sub-polynomial space, the strongest guarantee available is the $\ell_2$ guarantee, which requires finding all items that occur at least $\varepsilon\|f\|_2$ times in the stream, where the $i$th coordinate of the vector $f$ is the number of occurrences of $i$ in the stream. The first algorithm to achieve the $\ell_2$ guarantee was the CountSketch of [CCF04], which for constant $\varepsilon$ requires $O(\log n)$ words of memory and $O(\log n)$ update time, and is known to be space-optimal if the stream allows for deletions. Read More

We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\log^3 n)$ per edge insertion, $O(\log^4 n)$ per edge deletion, and $O(\log n/\log\log n)$ per query, where $n$ is the number of vertices. The previous best algorithm has worst case running time $O(\log^4 n)$ per edge insertion and $O(\log^5 n)$ per edge deletion. Read More

Does every Boolean tautology have a short propositional-calculus proof? Here, a propositional calculus (i.e. Frege) proof is a proof starting from a set of axioms and deriving new Boolean formulas using a set of fixed sound derivation rules. Read More