Lectures & Resources

Scribing:

Due by midnight next day after lecture. You have to use the following LaTeX template: scribe.tex. For a short introduction to LaTeX, see this mini-course. The scribed lecture will be posted immediately after it is received so that the rest of the class can use it before the following lecture. The staff will review the scribe, and, if necessary, the scriber(s) will be asked to rectify the lecture.

Schedule & Resources:

Jan 18: intro, approximate counting, Morris algorithm.

Lecture 1 scribe notes.

Other resources:

• scribe notes from a previous class.

Jan 23: approximate counting (cont). Hashing: universal and perfect.
Lecture 2 scribes.
Resources:

• wiki articles: https://en.wikipedia.org/wiki/Universal_hashing and https://en.wikipedia.org/wiki/Perfect_hash_function.

Jan 25: Hashing: power of 2 choices.
Lecture 3 scribes.
[HW1 assigned]. Resources:

• lecture notes from MIT 6.856 class (by Karger).

Jan 30: Sketching: Distinct Elements Count. Impossibility results.
Lecture 4 scribes.
Resources:

• lecture 2 from here.

Feb 1: Heavy Hitters, countMin algorithm.
Lecture 5 scribes.
Resources:

• lectures 3, 4 from here (and links therein).

Feb 6: Faster countMin, frequency moments.
Lecture 6 scribes.
Resources:

• lectures 3,7,8 from here (and links therein).

Feb 8: Dimension reduction, p-stable distributions.
Lecture 7 scribes.
[PS1 due, HW2 out]
Resources:

• lectures 3,7,8 from here (and links therein).

Feb 13: Nearest neighbor search: introduction.
Lecture 8 scribes.
Resources:

• lecture 10,11,12 from here (and links therein).

Feb 15: Nearest neighbor search: Locality Sensitive Hashing.
Lecture 9 scribes.
Resources:

• lecture 10,11,12 from here (and links therein).

Feb 20: [optional lecture]: advanced NNS algorithms.
Lecture slides: in pdf format and in pptx format.
Scribe notes.
Resources:

• lecture 12 from here (see both the slides and the scribe notes).
• see also these slides.
• the latest trade-off between space and query time (data-dependent) is in this paper.

Feb 22: Graph algorithms.
Lecture 10 scribes.
[PS2 due, HW3 out]
Resources:

• lectures 1,2 from these lecture notes by Williamson. see also his lectures 3,4 for applications of network flows.
• lecture 7 from Karger & Madry's class notes.
• sections 26.1, 26.2 from CLRS's "Introduction to Algorithms".

Feb 27: Graph algorithms.
Lecture 11 scribes.
Resources:

• lectures 2,5 from these lecture notes by Williamson.
• lecture 7 , lecture 8 from Karger & Madry's class notes.

Mar 1: Graph algorithms.
Lecture 12 scribes.
Resources:

• lectures 6,7 from these lecture notes by Williamson.
• lectures 8, lecture 9 from Karger & Madry's class notes.
• sections 26.4 from CLRS's "Introduction to Algorithms".

Mar 6: Spectral graph algorithms: adjacency matrix, random walks, eigenvalues, Rayleigh quotient.
Lecture 13 scribes.
Resources:

• Dan Spielman's class on Spectral graph algorithms (lecture 1).

Mar 8: Spectral graph algorithms: connections between eigenvalues and graph properties, top eigenvalues.
Lecture 14 scribes.
[PS3 due]
Resources:

• Dan Spielman's class on Spectral graph algorithms (lecture 3, 4).

[SB: Mar 13,15 SPRING BREAK]

Mar 20: Spectral graph algorithms: Laplacian graphs, drawing, cuts in graphs.
Lecture 15 scribes.
Resources:

• Dan Spielman's class on Spectral graph algorithms (lecture 2).

Mar 22: Spectral graph algorithms: Cheeger inequality and 2nd eigenvalue.
Lecture 16 scribes.
[project proposal due, HW4 out]
Resources:

• Dan Spielman's class on Spectral graph algorithms (lecture 6).

Mar 27: Linear programming: introduction, linear system of equations.
Lecture 17 scribes.
Resources:

• sections 2.2-2.4 of the Schrijver's course.
• lecture 13 from Karger & Madry's class at MIT.
• Erickson's class notes.

Mar 29: Linear programming: duality.
Lecture 18 scribes.
Resources:

• sections 2.2-2.4 of the Schrijver's course.
• lecture 14 from Karger & Madry's class at MIT.
• Erickson's class notes.

Apr 3: Linear programming: strong duality.
Lecture 19 scribes.
Resources:

• sections 2.2-2.4 of the Schrijver's course.
• lecture 14 from Karger & Madry's class at MIT.

Apr 5: Linear programming: simplex and ellipsoid algorithms.
Lecture 20 scribes.
Resources:

• notes from Aleksandar Nikolov's class.

[PS4 due]

Apr 10: Linear programming: gradient descent.
Lecture 21 scribes.
Resources:

• gradient descent: Nisheeth Vishnoi mini-course notes (chapter 1).
• a blog post on gradient descent, with momentum. has a nice tool to play with!
• Nesterov's notes (which also include lower bounds).

Apr 12: Linear programming: Newton's method, interior point algorithms.
Lecture 22 scribes.
Resources:

• Nisheeth Vishnoi mini-course notes (chapter 3).
• blog post by Sebastien Bubeck.

Apr 17: Linear programming: multiplicative weights update.
Lecture 23 scribes.
Resources:

• MWU: Nisheeth Vishnoi mini-course notes (chapter 2).

[project report (2) due, HW5 out]

Apr 19: Large-scale models: external memory.
Lecture 24 scribes.
Resources:

• Erik Demaine's lecture notes (L7).

Apr 24: Large-scale models: cache-oblivious, parallel algorithms.
Lecture 25 scribes.
Resources:

• cache-oblivious algorithms: E. Demaine's lecture notes (L7).
• parallel algorithms: lecture 27 from D. Karger and A. Madry's class.

Apr 26: Parallel algorithms (MapReduce/MPC). Class recap.
Resources:

• parallel algorithms: lecture 27 from D. Karger and A. Madry's class.
• parallel connectivity: see this lecture (pdf) from G. Yaroslavtsev's class.

May 1: lecture by Erik Waingarten on NNS under l_infty and metric embeddings.
[HW5 due]

May 12: final projects due.