Instructor | Hamed Hatami | |
TA's | Teaching assistants (TBA) are mainly responsible for grading the assignments. | |
Lecture | TBA | |
Outline | TBA | |
Office hours: | TBA. If you want to meet outside office hours, the best thing is to send me an email, but you can also just drop by my office, and if I'm not busy I will answer your questions. | |
Textbook | Jon Kleinberg and Eva Tardos, Algorithm Design, 2006 |
This course is an undergraduate course on advanced algorithmic techniques and applications. Topics include Network Flows, Linear programming, Complexity and NP-completeness, Approximation Algorithms, Randomized Algorithms, and Online Algorithms.
This is a rigorous course with an emphasis on mathematical proofs rather than implementations. The prerequisites are Comp 251 and one of Math 240/Math 235/Math 363. You must be comfortable with basic concepts from linear algebra, and you must be able to read and write precise mathematical statements.
Here are some questions that can help you decide if you have the background to take this course. If you have trouble understanding or answering these questions, in order to succeed in this course, you need to improve your background before enrolling in this course.
Homework (20% = 5 x 4%). There will be five homework assignments. The due dates are going to be announced. The homework and the exams will be graded based on correctness rather than effort alone. Each assignment will be posted on the course web page. Your grades will be posted on mycourses.
Late homeworks can be submitted until 48 hours after the deadline. There will be a penalty of -10 (out of 100) points for one-day delays, and -20 points for two-day delays on late homeworks unless a valid reason is provided by the student. Some personal circumstances for which accommodation may be warranted include, but are not limited to: Student illness (mental/physical), Family/partner illness, Death in the immediate family or of a person with whom the student has a similarly close relationship, Religious Observances, Pregnancy, Delivery of a child, Parenting issues.
The following are reasons for which an extension request will normally NOT be granted: Employment reasons, Travel/vacation/social plans, Airline flights and schedules, Other assignments and exams due on or about the due date.
Quizzes (9% = 3 x 3%). There will be 4 quizzes, and 3 out of 4 counts. The purpose of these quizzes is to enforce attendance, and to make sure that you are generally following the course.
Final grade is whichever of (Homework 20% + Quizzes 9% + Midterm 20% + final 51%) or (Homework 20% + Quizzes 9% + Midterm 10% + final 61%) that results in a better grade. However you must still receive a grade higher than 30% in the final exam in order to pass this course. Both midterm and final are closed-book, and closed-notes.
Class participation: Although not a formal component of the course grade, active participation can effect your grade in a positive way.
Your (i) background, your (ii) efforts, and more importantly (iii) the efficiency of your efforts will be the main determining factors on how well you will master the subject.
The grades are to give you some feedback, but you are the only person who can interpret them. They have some correlation with how well you have understood and learned the subject (that is why people will look at your grades, and GPA), but by no means this is definite. Some people are good at exams, and some are not, and we all have good days and bad days. Your main goal should be to acquire and improve your relevant problem solving skills rather than obtaining a good grade. The good grade hopefully will be a consequence of that.
Review | ||
Lecture | Topic | Reading |
1 | Background | |
Part I | ||
Lecture | Topic | Reading |
2 | The Ford-Fulkerson Algorithm | 7.1 |
3 | The Ford-Fulkerson Algorithm continued | 7.1 |
4 | Max flow-Min cut Theorem, correctness of the Ford-Fulkerson | 7.2 |
5 | Choosing good augmenting paths, Optional reading: the fattest path algorithm |
7.3 |
6 | Bipartite matching, Konig's theorem Theorem 3.14 here. | 7.5 |
7 | Konig's theorem, Disjoint path problem (directed). | 7.6 |
8 | Baseball elimination problem. | 7.12 |
9 | Baseball elimination problem finished. | 7.12 |
Part II | ||
Lecture | Topic | Reading |
10 | Linear programming. Formulating problems as LPs. | Some examples. |
11 | geometric interpretation of LP's. | Sections 1 and 2 of Luca Trevisan's Lecture 5. |
12 | midterm | |
13 | LP's in canonical form, introduction to duality. |
Finishing Lecture 5 and starting Lecture 6 from Luca's notes. |
14 | Strong duality. | Finishing Lecture 6 from Luca's notes. Dual in general. |
15 | Duality, Fractional vertex cover, and fractional matching, and Complementary slackness. | |
16 | Duality and MaxFlow-MinCut. | |
Part III | ||
Lecture | Topic | Reading |
17 | Shortest Path problem as a linear program. The complexity classes P and NP. | 8.3 |
18 | The complexity classes P, NP, CoNP, EXP, Efficient certifiers. | 8.3, 8.9 |
19 | Polynomial reductions, Cook-Levin: NP-completeness of SAT. | 8.3, 8.9 |
20 | NP-completeness of the Maximum Independent Set problem. | 8.1, 8.2, 8.4 |
21 | NP-completeness of Max Clique, Vertex Cover, 3SAT. | 8.2 |
22 | NP-completeness of Set Cover, 3-Colourability, k-Colourability, Hamiltonian cycle and path, Traveling Salesman Problem, SubsetSum. PSPACE, and QSAT | 8.2, 8.5, 8.7, 8.8, 8.10, 9 |
Part VI | ||
Lecture | Topic | Reading |
23 | A simple approximation algorithm for vertex cover, A 2-factor Approximation algorithm for Vertex Cover based on rounding LP. | 11.1, and this |
24 | Approximation algorithms for Load balancing and the center selection problem. | 11.1. 11.2 |
25 | A PTAS Approximation algorithm for the Knapsack problem. | 11.8 |
Academic honesty. McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offenses under the Code of Student Conduct and Disciplinary Procedures (see http://www.mcgill.ca/integrity for more information). Most importantly, work submitted for this course must represent your own efforts. Copying assignments or tests from any source, completely or partially, allowing others to copy your work, will not be tolerated, and they will be reported to disciplinary office.
Submission of written work in French. In accord [sic] with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.