CSC473 (Winter 2019): Advanced Algorithms

General Info

The lectures allow us to explain new material, how it relates to the rest of the course (and what you've learned in other courses), and to show examples of applying the material. Lecture notes that go into more details will be made available on this page.

Students often learn a lot from working with one another. You are encouraged to meet with other students from class for this purpose.

Lectures roughly fall into four main topics: randomized algorithms; linear programming and primal-dual algorithms; approximation algorithms; streaming algorithms.

Tentative Schedule of Lectures

Week	Topic	Readings
Week 1: Jan 7 –13	Monte Carlo Algorithms: Global Min-Cut	From "Algorithm Design" by Kleinberg and Tardos: Min Cut
Week 2: Jan 14–20	Finish Min Cut Las Vegas Algorithms: Closest Pair of Points	Karger-Stein Algorithm From "Algorithm Design" by Kleinberg and Tardos: Closest Pair of Points Finding triangles
Week 3: Jan 21–Jan 27	Approximate Near Neighbors	Approximate Near Neighbor Search
Week 4: Jan 28–Feb 3	Streaming Algorithms	Lectures notes on Streaming Algorithms
Week 5: Feb 4–10	Streaming Fingerprinting for String Matching	Lectures notes on Streaming Algorithms CLRS Section 32.2. Lecture Notes on Karp-Rabin
Week 6: Feb 11–17	Random Walks and Markov Chains	Lectures notes on Markov Chains You can also read the intro section of Chapter 4 of this book. Section 4.8 of the book covers PageRank. Linear Algebra Review Sheet
Feb 18–24	NO CLASS: Reading Week
Week 7: Feb 25–March 3	Finish Random Walks Linear Programming: Basics	LP Lecture notes
Week 8: March 4–10	Linear Programming Duality	LP Lecture notes Examples of LP formulations.
Week 9: March 11–17	Complementary Slackness Primal-Dual: the Hungarian Algorithm	Read M. Goemans's lecture notes.
Week 10: March 18–24	Finish the Hungarian Algorithm
Week 11: March 25–March 31	Deterministic and Randomized Rounding Algorithms Start Primal-Dual Approximation Algorithms	Sections 1.7, 5.1-5.2 of the Williamson and Shmoys book. All of Chapter 1 is recommended.
Week 12: Apr 1–5	Finish Primal-Dual Approximation Algorithms	Section 1.7 and 7.1-7.2 of the Williamson and Shmoys book.

Suggested Exercises

Suggested exercises from Williamson and Shmoys: 1.4, 1.5, 5.1, 5.2, 5.3, 5.6, 5.7, 7.2
- Hint for 7.2: You may need to sometimes remove edges from your set F during your algorithm in order to satisfy 2-approximate CS.
Do the exercises from Goemans's matchings lecture notes.
Suggested exercises for Min Cut:
- From Motwani and Raghavan's Randomized Algorithms (available through the U of T library at http://go.utlib.ca/cat/8230181) try the exercises 10.13 - 10.15 after Chapter 10.
- From Jeff Erickson's lecture notes, try the exercises after Lecture 14.
- Do the exercises in my lecture notes on the Karger-Stein Algorithm.
- After doing exercise 1 from Erickson's notes, try to give an O(m) time algorithm to execute the contraction algorithm, without using the Klein-Karger-Tarjan MST algorithm.