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Course

CS-450: Algorithms II

Lectures in this course (26)

Greedy Algorithms & Matroids

Introduces greedy algorithms and matroids, highlighting their efficiency in solving optimization problems.

Matroids: Matroid Intersection

Covers the concept of matroids, focusing on matroid intersection and the properties of subsets of a ground set.

Simplex Algorithm

Covers the Simplex algorithm for function minimization with linear constraints.

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Concentration Inequalities

Covers concentration inequalities and sampling methods for estimating unknown distributions, with a focus on population infection rates.

Pairwise Independence: Hashing and Load Balancing

Explores pairwise independence in hashing to avoid collisions and achieve load balancing.

Streaming Algorithms

Covers streaming algorithms, power of two choices, Misra-Gries estimator, and AMS sketch for frequency estimation.

Distinct Elements: Count and Hash Functions

Covers counting distinct elements using hash functions and the median trick.

Frequency Moments: Estimators and Algorithms

Covers the concept of frequency moments and introduces algorithms for estimating them efficiently.

Nearest Neighbor Search: Johnson-Lindenstrauss Lemma

Covers the Nearest Neighbor search algorithm and the Johnson-Lindenstrauss lemma for dimensionality reduction, exploring preprocessing techniques and locality-sensitive hashing.

Locality Sensitive Hashing

Explores Locality Sensitive Hashing for nearest neighbor search and submodularity in hash functions.

Unweighted Bipartite Matching

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.

Submodular Function Minimization

Covers submodular functions and their minimization, emphasizing diminishing returns and the Lovász Extension.

Convexity of Lovász Extension

Explores the convexity of Lovász extension and submodular function maximization, focusing on extending functions to convex sets and proving their convexity.

Submodular Maximization

Covers submodular function maximization using the greedy algorithm and its approximation guarantee.

Online Algorithms: Competitive Ratio

Covers online algorithms and competitive ratio in caching strategies to optimize memory usage.

Spectral Graph Theory: Introduction

Introduces Spectral Graph Theory, exploring eigenvalues and eigenvectors' role in graph properties.

Cheeger's Inequalities

Covers Cheeger's inequalities and the combinatorial properties of graphs.

Linear Programming: Weighted Bipartite Matching

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.