6.856J/18.416J Randomized Algorithms
Course Information
The course text is Randomized
Algorithms (link includes errata list). Copies should be
available at the Coop. You can also order online at Amazon or
Barnes
and Noble.
If you are thinking about taking this course, you might want to
see what past students have said about previous times I taught
randomized Algorithms, in
2007,
2005, or 2002, as well
as its sibling course Advanced
Algorithms.
Please register for the course by using this form.
You can send anonymous e-mail (praise, complaints, suggestions, ...)
to the 6.856 staff by using this form.
Handouts
- Course Summary and Info
- Problem Set 1, due 2/9/11
- Problem Set 2, due 2/16/11
- Problem Set 3, due 3/2/11
- Problem Set 4, due 3/9/11
- Problem Set 1 solutions
- Problem Set 2 solution
- Problem Set 3 solution
- Problem Set 5, due 3/16/11
- Problem Set 6, due 3/30/11
- Problem Set 4 solution
- Problem Set 5 solution
- Problem Set 7, due 4/6/11
- Course Project Assignment, due 4/6/11
- Problem Set 8, due 4/18/11
Notes
These notes reflect a starting plan that may change. They are my own lecture notes; they will not serve to teach
the material but should serve as a record of what was covered in each
lecture.
Note that all course notes can be found in nb, where you can read and
annotate them with questions.
- Lecture 1, 2/2. Introduction to Randomized Algorithms.
Quicksort, BSP, Min-cut.
PDF
and annotatable copy
- Lecture 2, 2/4. complexity theory, Adelman's theorem, game tree evaluation.
PDF
and annotatable copy
- Lecture 3, 2/7. game theory, lower bounds, Coupon collecting, stable marriage.
PDF
and annotatable copy
- Lecture 4, 2/9. Deviations: Markov, Chebyshev. Median Finding.
PDF
and annotatable
copy.
- 2/11, 2/14 cancelled
- Lecture 5, 2/16. Chernoff bound, load balancing
(PDF
and annotatable
copy), Randomized routing
(PDF
and annotatable
copy)
- 2/18,20,22 cancelled
- Lecture 6, 2/28. Two-choice load balancing.
PDF,
and annotatable copy
- Lecture 7, 3/2.
Hashing: annotatable
or download,
Perfect/Cuckoo/Consistent: annotate
or download. Scribe
notes: annotate,
download
- Lecture 8, 3/4. Fingerprinting. String Matching. Bloom Filters
(annotate, download).
Scribe notes:
(annotate, download)
- Lecture 9, 3/7. Fingerprinting II. Polynomials. Perfect Matching.
(annotate, download)
- Lecture 10, 3/9. Symmetry Breaking. Shortest
Paths (annotate, download). Finding perfect matchings.
Independent set (annotate,
download)
- Lecture 11, 3/11. Sampling (annotate, download).
- Lecture 12, 3/14. Streaming (annotate, download).
- Lecture 13, 3/16. Rare Events. DNF Counting
(annotate, download). MST
(annotate, download).
- Lecture 14, 3/18. Counting Versus Generation.
(annotate, download).
Minimum Cut (textbook).
- 3/21-3/25 spring break
- Lecture 15, 3/28. Minimum Cut.
(annotate, download).
Scribe notes (annotate, PDF).
- Lecture 16, 3/30. Graph sparsification.
Network reliability. No notes, but papers:
Sparsification
(annotate, download),
Reliability
(annotate, download).
- Lecture 17, 4/1. Geometry. Arrangements of Lines. Randomized
Incremental Construction: Convex Hull
(annotate, download)
- Lecture 18, 4/4. Trapezoidal Decomposition. Sampling for LP.
(annotate, download)
- Lecture 19, 4/6. LP continued. Iterative reweighting. Randomized incremental
construction. Hidden Dimension.
(annotate, download)
- Lecture 20, 4/8. Approximation algorithms. Randomized
Rounding. Max-cut, Max-SAT, Set Cover, Disjoint routing.
(annotate, download)
Intentions going forward:
- Lecture 18, 4/8. Derandomization.
PDF,
- Lecture 19, 4/11. Embeddings.
PDF,
- Lecture 20, 4/13. Markov Chains.
PDF,
- Lecture 21, 4/15. Expanders.
PDF,
- Lecture 22, 4/?. Markov Chains II.
PDF,