Las Vegas & Monte Carlo algorithms; inequalities of Markov, Chebyshev, Chernoff; negative correlation; Markov chains: convergence, rapidly mixing; generating functions; Examples include: min cut, median, balls and bins, routing in hypercubes, 3SAT, card shuffling, random walks
Learning objective
After this course students will know fundamental techniques from probabilistic combinatorics for designing randomized algorithms and will be able to apply them to solve typical problems in these areas.
Content
Randomized Algorithms are algorithms that "flip coins" to take certain decisions. This concept extends the classical model of deterministic algorithms and has become very popular and useful within the last twenty years. In many cases, randomized algorithms are faster, simpler or just more elegant than deterministic ones. In the course, we will discuss basic principles and techniques and derive from them a number of randomized methods for problems in different areas.
Lecture notes
Yes.
Literature
- Randomized Algorithms, Rajeev Motwani and Prabhakar Raghavan, Cambridge University Press (1995) - Probability and Computing, Michael Mitzenmacher and Eli Upfal, Cambridge University Press (2005)
Performance assessment
Performance assessment information (valid until the course unit is held again)
The performance assessment is only offered at the end after the course unit. Repetition only possible after re-enrolling.
Additional information on mode of examination
Exercises 30% to the final grade: In week 4, 7 and 10 of the term (roughly) we will hand out a specially marked exercise, whose solution (typeset in LaTeX or similar) is due two weeks later. These solutions will be graded; the grades will each account for 10% of the final grade.
End of term: written exam (180 min) accounting for 70% of the grade; open book exam: you are allowed to consult any books, handouts, and personal notes. The use of electronic devices is not allowed.
Learning materials
No public learning materials available.
Only public learning materials are listed.
Groups
No information on groups available.
Restrictions
There are no additional restrictions for the registration.
Performance assessment as a semester course