A weighted pseudorandom generator (WPRG) is a generalization of a pseudorandom
generator (PRG) in which, roughly speaking, probabilities are replaced with weights that are …

The notion of the derandomized square of two graphs, denoted as G s H, was introduced by
Rozenman and Vadhan as they rederived Reingold's Theorem, SL= 𝐋. This pseudorandom …

In a recent work, Chen, Hoza, Lyu, Tal and Wu (FOCS 2023) showed an improved error
reduction framework for the derandomization of regular read-once branching programs …

Spectral sparsification for directed Eulerian graphs is a key component in the design of fast
algorithms for solving directed Laplacian linear systems. Directed Laplacian linear system …

Abstract The Kadison-Singer Conjecture, as proved by Marcus, Spielman, and Srivastava
(MSS)[1], has been informally thought of as a strengthening of Batson, Spielman, and …

Randomness is a powerful resource in computer science, with rich applications in algorithm
design, cryptography, distributed computing, etc. Most of the applications assume access to …

Graph sparsification is the concept of using a sparse graph to approximate a much denser
one---a powerful tool for improving the complexity of graph algorithms. In this thesis, we …