Randomized Algorithms (semester 2019A)

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

Course description

Instructors: Robert Krauthgamer and Moni Naor

Grader: Ohad.Trabelsi (at weizmann.ac.il)

When and where: Thursday 14:15-17:00, Ziskind Lecture Room 1

First class: Nov. 8, 2018

FGS code: 20194201

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: There will be a final assignment (take-home exam).
Here is the final exam itself.

Webpage: http://www.wisdom.weizmann.ac.il/~robi/teaching/2019a-RandomizedAlgorithms

Previous offerings:
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

• [posted 2019-02-07] the instructions for the final (take-home exam) will be similar to this 2017 course.
  
• [posted 2019-01-04] Take-home exam rescheduled: distributed Feb. 25, due within 3 days
• [posted 2018-12-28] Take-home schedule: distributed Feb. 10, due within 3 days
  
• [posted 2018-12-24] Problem Set 2 was corrected (in Q.#2) with extended due date
  
• [posted 2018-11-20] The class of Nov. 29 is moved (room change) to Wolfson Hall 
  

Lectures

1. 2018-11-08, Moni: (Multi)-Set Equality, Closest Pair, Minimum Cut.
   Reading: lecture notes #1
2. 2018-11-15, Robi: Random Walks on Graphs
   Reading: lecture notes #2, see also [MR, chapter 6]
   Further reading: [Levin, Peres, and Wilmer, chapter 9], [Doyle and Snell, also as arXiv:math/0001057], [Lyons and Peres, chapter 2]
3. 2018-11-22, Robi: Effective Resistance and an Algorithm for 2SAT
   Reading: lecture notes #3, see also [MU, chapter 7]
   Further reading: [Feige, slides on cover time]
   
4. 2018-11-29, Ohad: 2-Universal Hash Families and Perfect Hashing
   Reading: [MU, chapter 13.3]
5. 2018-12-06, Moni: Maximal Independent Set, Analysis of Randomized Quicksort, Extractors and Probabilistic Constructions
   Reading: lecture notes #5
6. 2018-12-13, Moni: Cuckoo Hashing, k-Wise Independence and Extractor Constructions
   Reading: class slides 
7. 2018-12-20, Robi: Importance Sampling and Coresets for Clustering
   Reading: lecture notes #7, see also [MR, chapters 11.2], [Munteanu and Schwiegelshohn, survey on coresets]
   
8. 2018-12-27, Robi: Coresets via Uniform and Importance Sampling 
   Reading: lecture notes #8, see also [Munteanu and Schwiegelshohn, survey on coresets]
   
9. 2019-01-03, Robi: Edge-Sparsification of Hypergraphs and Some Occupancy Problems  
   Reading: lecture notes #9, see also [MR, chapters 3.1, 3.2, 3.6 and 4.1], [DP, chapter 1.6]
10. 2019-01-10, Moni: TBA
11. 2019-01-17, Moni: TBA
12. 2019-01-24, Moni: TBA
13. 2019-01-31, Robi: Dimension Reduction in l_2
    Reading: lecture notes #13
    Further reading: [Dasgupta and Gupta], [Jiri Matousek (lecture notes), chapter 2]
    
14. 2019-02-07, Robi: The JL Transform and Oblivious Subspace Embedding
    Reading: lecture notes #14
    Further reading: [Woodruff, section 2, also as arXiv:1411.4357] 

Assignments

• Problem set 1 (posted Nov. 23)
  
• Problem set 2 (posted Dec. 15, corrected Dec. 24), note the extended due date
• Problem set 3 (posted Jan. 4)

Reading material

Relevant textbooks:

• [MR] Randomized Algorithms by Motwani and Raghavan (errata).
• [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) -- available online 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:

• The Probabilistic Method by Alon and Spencer (3rd Edition).
• Concentration by Colin McDiarmid. Probabilistic Methods for Algorithmic Discrete Mathematics, 1998, 1-46.
• Probability and Random Processes (2nd ed.) by Grimmett and Stirzaker.