Lecture Notes on Randomized Linear Algebra

Lectures on Randomized Numerical Linear Algebra

This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.

Lecture Notes on Spectral Graph Methods

These are lecture notes that are based on the lectures from a class I taught on the topic of Spectral Graph Methods at UC Berkeley during the Spring 2015 semester.

Lecture Notes on Quantum Algorithms

The lecture notes contain three parts. The first part is Grover's Search Algorithm with modifications, generalizations, and applications. The second part is a discussion on the quantum fingerprinting technique. The third part is Quantum Walks (discrete time) algorithm with applications.

大规模数据算法——讲义

Algorithms for Massive Data -- Lecture Notes

本讲义介绍处理大规模数据的算法技术，包括压缩数据结构、数据草图、后缀数组、概率过滤器、局部敏感哈希及流算法等。

Lecture Notes on the ARV Algorithm for Sparsest Cut

One of the landmarks in approximation algorithms is the $O(\sqrt{\log n})$-approximation algorithm for the Uniform Sparsest Cut problem by Arora, Rao and Vazirani from 2004. The algorithm is based on a semidefinite program that finds an embedding of the nodes respecting the triangle inequality. Their core argument shows that a random hyperplane approach will find two large sets of $Θ(n)$ many nodes each that have a distance of $Θ(1/\sqrt{\log n})$ to each other if measured in terms of $\|\cdot \|_2^2$. Here we give a detailed set of lecture notes describing the algorithm. For the proof of the …