## Design and Analysis of Algorithms

Instructor: Vitaly Skachek, office hours: Paabel 224, Monday 10:15 - 12:15, or by appointment

Teaching assistants: Behzad Abdolmaleki, Mozhgan Pourmoradnasseri

Lecture: Mon. 14.15 - 16.00, J. Liivi 2 - 122

Practice: Mon. 16.15 - 18.00, Paabel 219, or Tue. 16.15 - 18.00, Paabel 218, or Thur. 14.15 - 16.00, Paabel 220

Language of instruction: English

### Midterm exam

A midterm exam will take place on Monday, November 11th, between 14:15-15:55 (during the lecture time). The total duration of the exam is 1 hour and 40 minutes. The exam will take place in rooms J. Liivi 2-122, -224, and -512.

Any written and printed material is allowed in the exam. No electronic devices are allowed (no phones, computers, tablets, calculators, etc.)

Due to room constraints, please register to one of the exam rooms (122, 224 or 512) as soon as possible. If you cannot register for some reason -- please notify Vitaly without delay.

### Announcements

**Old announcements:**

- Change of room due to the Institute Day on Thursday, October 3rd: the practice session will take place in J. Liivi 2, room 207.

### Literature

- S. Dasgupta, C. Papadimitriou and U. Vazirani,
, McGraw Hill, New York 2008.*Algorithms* - V.V. Vazirani,
, Springer-Verlag, Berlin 2003.*Approximation Algorithms* - S. Even,
, 2nd edition, Cambridge University Press, New York 2012.*Graph Algorithms* - T.H. Cormen, C.E. Leiserson, R.L. Rivest and C. Stein,
, MIT Press, Boston 2009.*Introduction to Algorithms*

### Course description

This course focuses on design and analysis of advanced algorithms in computer science. It is advised to take **Algorithms and Data Structures** (MTAT.03.133) and **Advanced Algorithmics** (MTAT.03.238) before you take this course or in parallel. In comparison to "Advanced Algorithmics", this course will emphasize the analysis of the algorithms (proof of correctness, complexity analysis), and will **not** focus on implementations and programming.

### Grading policy

There will be six homeworks, the midterm and final exam. The final grade will be based on the grade of homeworks (30%), of the midterm (30%), and of the final exam (40%). The homeworks will mainly contain questions of design and of analysis of algorithms, and typically will **not** contain programming tasks.

### Exam dates

- Midterm: November 11 at 14:15-16:00 (during the lecture time).
- Final exam: December 16 at 14:15-16:15 or January 13 at 14:15-16:15.

### Syllabus

The following is a preliminary list of topics (some deviations from this list are possible):

#### Part 1: Deterministic algorithms

- Fast Fourier transform. Algorithm for fast multiplication of polynomials.
- Algorithms for finding a minimum spanning tree in a graph.
- Flow networks. Efficient algorithm for finding a maximum flow in a network.
- Finding maximum flow in 0-1 network.
- Finding a minimum cost flow. Finding a minimum cost matching in a bipartite graph.
- Linear programming. Feasible solution. Primal and dual problem.

#### Part 2: Approximation algorithms

- Approximation algorithm for set cover problem.
- Travelling salesman problem.
- Knapsack problem.
- Linear programming in approximation algorithms.
- Linear programming approach to set cover problem.
- Primal-dual approach.