Comp 360 Algorithm Design

 
Instructor   Hamed Hatami
TA's   Teaching assistants (Konrad Anand, Pouriya Alikhani, Vincent Luczkow, Jason Hu) are mainly responsible for grading the assignments.
Lecture   Monday-Wednesday 16:05 -17:25 PM at ENGMC 304
Outline course outline
Office hours:   See the calendar. Wednesdays 2:30-3:30pm in McConnell 308. 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

Description

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.

Video recording: I was not sure if I should continue recording my lectures, since it seemed to have caused a drop in the attendance, and an instructor relies on the feedback from the students at the class to pace the course, and explaining the tricker material properly. However since I think the recordings are a good resource for reviewing the course, I decided to record the lectures, but we will have some easy suprise quizzes in the class to keep the attendance high.

Grading

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.

Surprise quizzes (9% = 3 x 3%). There will be 4 surprise quizzes in the class, 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.

Some advice on how to do well in this course:

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.

Course Schedule

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 cannonical 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-completness of the Maximum Independent Set problem. 8.1, 8.2, 8.4
21 NP-completness of Max Clique, Vertex Cover, 3SAT. 8.2

Assignments and exams

Policies

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.