Randomized Algorithms (semester 2025A)

[Course description] [Announcements] [Lectures] [Assignments] [Reading material]

Course description

Instructors: Robert Krauthgamer and Moni Naor

Grader: Guy Kornowski (at weizmann.ac.il)

When and where: Monday 14:15-17:00, Ziskind Lecture Room 155 

First class: Nov. 4, 2024 

FGS code: 20254071

Syllabus: Algorithms that are randomized, i.e., use coin tosses during their execution, are central in many computational scenarios, and have become a key tool in Theoretical Computer Science and in application areas. The course will cover the development and use of such probabilistic techniques, including some of the following topics: Concentration results; Simulating randomness, in particular limited independence; Load balancing; Routing algorithms; Randomized rounding; Sampling and sublinear algorithms; Algorithms in the data stream model; Communication protocols and the sketching model.

Prerequisites: Students are expected to be familiar with algorithms, complexity theory, probability theory, and linear algebra, at an undergraduate level.

Final: The final assignment will be a take-home exam.
Here is the final exam itself.

Webpage: http://www.wisdom.weizmann.ac.il/~robi/teaching/2025a-RandomizedAlgorithms

Previous offerings:
http://www.wisdom.weizmann.ac.il/~robi/teaching/2023a-RandomizedAlgorithms
http://www.wisdom.weizmann.ac.il/~robi/teaching/2021a-RandomizedAlgorithms
http://www.wisdom.weizmann.ac.il/~robi/teaching/2019a-RandomizedAlgorithms
http://www.wisdom.weizmann.ac.il/~robi/teaching/2017a-RandomizedAlgorithms
http://www.wisdom.weizmann.ac.il/~robi/teaching/2015a-RandomizedAlgorithms
http://www.wisdom.weizmann.ac.il/~robi/teaching/2013a-RandomizedAlgorithms
http://www.wisdom.weizmann.ac.il/~robi/teaching/2011a-RandomizedAlgorithms

Announcements

• During the semester, the course material is available only on moodle (and copied to here eventually)
  

Lectures

1. 2024-11-04, Moni: Introduction and the Min Cut algorithm.
   Class material: lecture notes #1.  
   
2. 2024-11-11, Moni:  A better exponential time algorithm for satisfiability, streaming, Freivalds Matrix Checking SAT.
   Class material: lecture notes #2.
   
3. 2024-11-18, Moni: Large Deviation Bounds, Communication Complexity and Existential Proofs via Probabilistic Construction Communication.
   Class material: lecture notes #3.
   
4. 2024-11-25, Robi: Dimension Reduction in l_2 fast JL.
   Class material: lecture notes #4.
   
5. 2024-12-02, Robi: JL Transform, Oblivious Subspace Embedding, and Least Squares Regression.
   Class material: lecture notes #5.
   
6. 2024-12-09, Robi: Nearest Neighbor Search in l_1.
   Class material: lecture notes #6.
   
7. 2024-12-16, Robi: Probabilistic Embedding into Dominating Trees.
   Class material: lecture notes #7.
   
8. 2024-12-23, Robi + Moni: Probabilistic Embedding into Dominating Trees (cont'd) + Cuckoo Hashing.
   Class material: lecture notes #8a. Class +  lecture notes #8b.
9. 2024-12-30, Moni: Cuckoo Hashing (cont'd) and Bloom Filters.
   Class material: lecture slides #9.
   
10. 2025-01-06, Moni: Lovasz Local Lemma.
    Class material: lecture slides #10.
11. 2025-01-14, Moni: Card Guesing.
    Class material: lecture slides #11.
12. 2025-01-20, Robi: Importance Sampling, Counting DNF solutions, and Coresets for Clustering.
    Class material: lecture notes #12.
13. 2025-01-27, Robi: Coresets via Importance Sampling.
    Class material: lecture notes #13.

Assignments

• Problem set 1 and notes/solutions
  
• Problem set 2 and notes/solutions
• Problem set 3
• Problem set 4

Reading material

Relevant textbooks:

• [MR] Randomized Algorithms by Motwani and Raghavan (errata) -- eBook available inside Weizmann.
  
• [MU] Probability and Computing: Randomized Algorithms and Probabilistic Analysis by Mitzenmacher and Upfal (errata).
• [DP] Concentration of Measure for the Analysis of Randomized Algorithms by Dubhashi and Panconesi (errata) -- eBook available inside Weizmann.
• [AS] The Probabilistic Method by Alon and Spencer (4th Edition) -- eBook available inside Weizmann (2nd Edition).
• [RY] Communication Complexity and Applications by Rao and Yehudayoff -- eBook available inside Weizmann.
  

Similar courses (many with lecture notes):

• Randomized Algorithms by Nicholas Harvey at UBC (2015)
  
• Randomized Algorithms by Sariel Har-Peled at UIUC (2014)
• Randomized Algorithms and Probabilistic Analysis by James R. Lee at UW (2016)
• Randomized Algorithms by Avrim Blum and Anupam Gupta at CMU (2011)
  
• Randomized Algorithms by David Karger at MIT (2015)

Useful references:

• Concentration by Colin McDiarmid. Probabilistic Methods for Algorithmic Discrete Mathematics, 1998, 1-46.
• Probability and Random Processes (2nd ed.) by Grimmett and Stirzaker.