
About Course
Randomized Algorithms.
Algorithms are required to be “correct” and “fast”. In a wide variety of applications, these twin objectives are in conflict with each other. Fortunately, neither of these ideals is sacrosanct. Therefore we can often try to optimize one of these goals by incurring a small penalty on the other. This takes us to the field of Randomized Algorithms. Often, the randomized variants, in addition to being faster than their deterministic counterpart, are simpler to understand and implement. In this course, we will study the tradeoff between correctness and speed. We will be learning a number of methods to design and analyze randomized algorithms.
INTENDED AUDIENCE: Senior UG students, PG students, and Ph.D. candidates interested in computer science, combinatorics, etc.
Course Content
Randomized Algorithms
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Randomized Algorithms [Intro Video]
00:00 -
Lecture 1: Introduction to Randomized Algorithms
00:00 -
Lecture 2: Randomized Mincut Algorithm
00:00 -
Lecture 3: Randomized Find
00:00 -
Lecture 4: Probability Review
00:00 -
Lecture 5: Expectation of Random Variables
00:00 -
Lec 6: Conditional Probability and Conditional Expectation2
00:00 -
Lec 7: Birthday Paradox
00:00 -
Lecture 8: Markov and Chebychev’s Inequalities
00:00 -
Lecture 9: Median Algorithm
00:00 -
Lecture 10: Chernoff Bound
00:00 -
Lec 11: Permutation Routing on a Hypercube
00:00 -
Lec 12: Permutation Routing on a Hypercube(Analysis)
00:00 -
Lec 13: Introduction to Probabilistic Method
00:00 -
Lec 14: More Examples on Probabilistic Method
00:00 -
Lec 15: Lovasz Local Lemma
00:00 -
Lec 16: Introduction to Markov Chains
00:00 -
Lec 17: 2-SAT and Markov Chains
00:00 -
Lec 18: 3-SAT and Markov Chains
00:00 -
Lec 19: Electrical Networks
00:00 -
Lec 20: Cover Time
00:00 -
Lec 21: Rapid Mixing
00:00 -
Lec 22: Introduction to Computational Complexity
00:00 -
Lec 23: Pratt’s Certificate
00:00 -
Lec 24: Primality Testing
00:00 -
Lec 25: Miller Rabin Algorithm
00:00 -
Lec 26: All pair shortest path-I
00:00 -
Lec 27: All pair shortest path-II
00:00 -
Lec 28: Randomized MST
00:00 -
Lec 29: Introduction to approximate counting
00:00 -
Lec 30: DNF counting
00:00 -
Lec 31: Perfect Matching-I
00:00 -
Lec 32: Perfect Matching-II
00:00 -
Lec 33: Perfect Matching-III
00:00 -
Lec 34: Treaps
00:00 -
Lec 35: Hashing
00:00 -
Lec 36: Probabilistically checkable proofs – I
00:00 -
Lec 37: Probabilistically checkable proofs – II
00:00 -
Lec 38: Probabilistically checkable proofs – III
00:00 -
Lec 39: LFKN Protocol
00:00 -
Lec 40: Summary
00:00