**ALGORITHMS AND
COMPLEXITY**

**CS 3AC3 (Winter 2018)**

*** * * This outline
is constantly updated. Students should consult this page
regularly for all information relevant to this course * * ***

**Instructor**

Dr. George Karakostas

ITB/218, ext 26132, Mac address: karakos

Office hours: TBA (by email appointment)

**Course Assistance**

Enamul Haque (haquee@mcmaster.ca)

Yasami Sartipi (yasamin.sartipi@gmail.com)

**Schedule**

Term II, 2017/18

Tu We Fr 12:30 - 1:20 PM, Rm T13 127

**Tutorials
**

Session
1: Mo 1:30 - 2:20 PM, Rm BSB 119

**Prerequisites**

**CS 2C03, CS 2FA3**

Course Objectives

In this course, we
will study the solution of computational problems from two
complementary perspectives: (i) The **Algorithm Design &
Analysis **perspective, i.e., the design methods one can
employ in order to build efficient algorithms for fundamental
problems (e.g., network flows), and the analysis of their
running times. We will study the design of Divide-and-Conquer,
Greedy and Dynamic Programming algorithms, approximations
algorithms that are efficient but can only provide
approximation-of-the-optimal guarantees, and the use of
randomization in our algorithms. (ii) The **Computational
Complexity **perspective, i.e., the study of the inherent
difficulty of solving a problem computationally. As opposed to
the 'easyness' of solving a problem, demonstrated by efficient
algorithms designed in (i), in this part we will study how one
can show that a problem is at least as 'hard' to solve as
another problem, using reductions, and will classify our
problems into complexity classes such as P, NP, PSPACE,
according to their 'hardness'.

More specifically, students should know and understand:

- Worst case analysis of algorithms
- Divide-and-Conquer algorithms
- Greedy algorithms
- Dynamic Programming
- Network Flows
- Turing-Church Thesis, complexity classes (P, NP, PSPACE)
- Approximation algorithms
- Randomized algorithms

Students should be able to

- Analyze the running time of algorithms
- Design Divide-and-Conquer algorithms
- Design Greedy algorithms
- Design Dynamic Programming algorithms
- Solve Network Flow problems
- Distinguish problems according to their complexity class
- Design simple approximation algorithms
- Use randomness in algorithms

**Learning
objectives, indicators, and rubrics**** **

**Outline of Topics
(roughly per week)**

- Analysis of algorithms (Chapter 2, slides, KT slides)

- Divide-and-Conquer and recurrences, the class P
(5.1 - 5.5, KT slides)

- Greedy algorithms (4.1 - 4.7, slides, KT slides)
- Dynamic Programming (Chapter 6, slides, KT slides)

- Network Flow (7.1-7.3, 7.5-7.12, KT slides1, KT slides2)

- Turing Machines, the Turing-Church Thesis, the class NP (Chapter 8, slides, KT slides1, KT slides2, KT slides3)
- The class PSPACE (Chapter 9, KT slides)
- Approximation algorithms (11.1 - 11.3, 11.8, KT slides)
- Randomized algorithms (13.1- 13.5, KT slides)

**Student Assessment
(Grading)**

- Homework assignments
**15%** - Midterm
exam
**40%****(Open book (only original hardcopy of the textbook, no notes))** - Final
exam
**45%****(Open book (only original hardcopy of the textbook, no notes))**

**Policy on
collaboration for homework assignments: **Collaboration
on the homework assignments is highly encouraged, within
reasonable limits. Students are expected to discuss assignment
problems with each other, and to cooperate on solutions in
groups of no more than 5 people. However, the final write-up
should be done by individual students (i.e. individual
students should be able to explain their solutions by
themselves, if such an explanation is asked for by the
instructor) and the names of the collaborators should appear
on the paper. Cooperation and teamwork are necessary for the
success of any complex task (the design of algorithms being
one such task), and it is the instructor's hope that students
will come to appreciate them in a constructive way. Please see
the instructor if you need someone to collaborate with.

**Policy on delayed
assignments: **Assignments delivered between the lecture
they were due and the following lecture get 50% of total
credit. After the following lecture, no credit given.

**Policy on
collaboration during exams: ****ABSOLUTELY
NO COLLABORATION DURING EXAMS!!!**

**Resources**

**Required textbook:**
**"Algorithm Design", by J. Kleinberg and E. Tardos,
Addison-Wesley **

**Recommended textbook: "Introduction to Algorithms", 3rd
Ed., by T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C.
Stein, MIT Press
Recommended textbook: "Introduction to the Theory od
Computation", 3rd Ed., by M. Sipser, Cengage Learning**

**Academic
Dishonesty**

**"Academic
dishonesty consists of misrepresentation by deception or by
other
fraudulent means and can result in serious consequences,
e.g. the grade of
zero on an assignment, loss of credit with a notation on the
transcript
(notation reads: "Grade of F assigned for academic
dishonesty"), and/or
suspension or expulsion from the university.
It is your responsibility to understand what constitutes
academic
dishonesty. For information on the various kinds of
academic dishonesty
please refer to the Academic Integrity Policy, specifically
Appendix 3,
located at
http://www.mcmaster.ca/senate/academic/ac_integrity.htm
The following illustrates only three forms of academic
dishonesty:
1. Plagiarism, e.g. the submission of work
that is not one's own or for which other credit has been
obtained. (e.g. submitting a copy of someone else's
writeup for an assignment)
2. Improper collaboration in group work.
(e.g. collaboration between groups in an assignment)
3. Copying or using unauthorized aids in
tests and examinations."
**

**Faculty Notice
**

**"The Faculty of Engineering is
concerned with ensuring an environment that is free of all
discrimination. If there is a problem, individuals are
reminded that they should contact the Department Chair, the
Sexual Harrassment Officer or the Human Rights Consultant, as
the problem occurs."
**

**"The instructor and university
reserve the right to modify elements of the course during
the term. The university may change the dates and deadlines
for any or all courses in extreme circumstances. If either
type of modification becomes necessary, reasonable notice
and communication with the students will be given with
explanation and the opportunity to comment on changes. It is
the responsibility of the student to check their McMaster
email and course websites weekly during the term and to note
any changes."
**

**Assignments
**

All assignments are
to be submitted to the dropbox for CS 3AC3 on the first floor
of the ITB building.

TBA

To read the
assignment files, you'll need the Adobe Reader, which is here.

**Slides**

The lecture slides
used in the lectures are designed by the textbook authors, and
are distributed by Pearson Addison-Wesley.