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COMP5270 · S1 2026
Randomised & Advanced Algorithms
Interactive study guides with simulations, proofs, quizzes, and bilingual support — built from lecture notes, slides, and tutorials.
Coverage
12 structured chapters
Toolkit
Study guides, proofs, simulations
Format
Lecture notes + problem sets + simulation synthesis
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Chapter 1
Randomness, Probability & Algorithms
Randomized algorithms, Las Vegas vs Monte Carlo, QuickSort analysis, indicator variables, and the probability toolkit.
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10 Problems
EN / 中文
Chapter 2
Concentration Bounds, and Tricks
Markov, Chebyshev, Chernoff bounds, and tail inequality techniques for analyzing randomized algorithms.
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11 Problems
EN / 中文
Chapter 3
Balls in Bins
The balls-into-bins model, birthday paradox, coupon collector, load balancing, and power of two choices.
Ready
10 Problems
EN / 中文
Chapter 4
Derandomisation
Method of conditional expectations, pairwise independence, and converting randomized algorithms to deterministic ones.
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8 Problems
EN / 中文
Chapter 5
Graph Algorithms
Karger's Min-Cut, Karger-Stein algorithm, counting minimum cuts, and expected linear-time MST.
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7 Problems
EN / 中文
Chapter 6
🗄️ Hashing and Friends
Hash tables, universal & strongly universal hash families, collision handling (chaining, open addressing, cuckoo hashing), and Bloom filters.
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7 Problems
Bloom Filter Sim
EN / 中文
Chapter 7
📍 Nearest Neighbours & Dimensionality Reduction
Nearest neighbour problem, Johnson-Lindenstrauss lemma for dimensionality reduction, locality-sensitive hashing (LSH), and approximate nearest neighbours.
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7 Problems
JL Demo
EN / 中文
Chapter 8
🌊 Streaming and Sketching I
Streaming algorithms: Misra-Gries frequency estimation, Morris counter for approximate counting, and Tidemark/BJKST for distinct elements.
Ready
8 Problems
Morris Sim
EN / 中文
Chapter 9
📊 Streaming and Sketching II
Sketching algorithms, CountSketch with ℓ₂ guarantee, CountMinSketch with ℓ₁ guarantee, turnstile model, and linear sketches.
Ready
7 Problems
CountSketch Sim
EN / 中文
Chapter 10
📈 Linear Programming & Randomised Rounding
LP relaxation, ILP formulation, randomised rounding for Min-Cut, Max-SAT approximation (1/2, 1-1/e, 3/4), and AM-GM inequality.
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7 Problems
Max-SAT Demo
EN / 中文
Chapter 11
📊 Learning and Testing Distributions
Total variation distance, learning distributions in O(k/ε²), uniformity testing in O(√k/ε²), collision-based testers, and identity testing.
Ready
8 Problems
Uniformity Tester
EN / 中文
Chapter 12
🧠 Learning from Experts
Expert advice, halving algorithm, multiplicative weights update (MWU), randomised MWU, potential function arguments, and regret bounds.
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6 Problems
MWU Sim
EN / 中文