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 are 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 this 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.PRE-REQUISITES : Basic Understanding of Algorithms and ProbabilitylINDUSTRY SUPPORT : Google, Microsoft

COURSE LAYOUT

Week 1 : Introduction to Randomized Algorithms
Week 2 : Probability Review
Week 3 : Moments and Deviation
Week 4 : The Probabilistic Method
Week 5 : Markov Chains - I
Week 6 : Markov Chain - II
Week 7 : Number Theoretic Algorithms
Week 8 : Graph Algorithms
Week 9 : Approximate Counting
Week 10: Data Structures
Week 11: Computational Complexity
Week 12: Review of the course