Understanding Samplers and Hitting Sets in Randomized Algorithms

Randomness is a cornerstone of modern algorithm design, enabling faster computation and powerful approximations. This text-based course introduces the core concepts of pseudorandomness, focusing on how samplers and hitting sets allow algorithms to efficiently approximate properties and reduce reliance on true random bits. You will build a solid theoretical foundation by examining how different sampling mechanisms balance randomness efficiency and accuracy. Starting with elementary definitions, you will explore how combinatorial objects like expander graphs enable powerful derandomization techniques. What you'll learn: - Understand the formal definitions and significance of samplers and hitting sets in randomized computation - Analyze naive sampling versus pairwise-independent sampling methods - Apply the median-of-means technique to amplify statistical confidence and bound error - Explore the construction of Boolean samplers using expander graph properties - Construct hitting sets directly from samplers to solve search and decision problems - Examine modern principles of randomness reduction and derandomization The course begins with foundational probability and terminology before progressing through structured mathematical explanations and analytical exercises. Designed for curious learners, computer science students, and programmers seeking a rigorous yet accessible entry into pseudorandomness without requiring advanced prerequisites. Start reading to deepen your understanding of randomized algorithms and pseudorandomness today.