Design and Analysis of Algorithms
Instructor: Vitaly Skachek, Wed 10.30-11.30, or by appointment
Teaching assistants: Sander Mikelsaar, Karan Khathuria, Javier Gil Vidal
Lecture (Delta bld. room 1021): Wednesday 12.15 - 13.45 (both in-person and online)
Monday 12.15 - 13.45 (both in-person and online): Delta room 2048
Thursday 14.15 - 15.45 (in-person): Delta room 2010
Friday 12.15 - 13.45 (in-person): Delta room 2010
Language of instruction: English
Main mode of communications: Moodle
- There will be no class on Monday, August 29th. The first class will be on Wednesday, August 31st.
- S. Dasgupta, C. Papadimitriou and U. Vazirani, Algorithms, McGraw Hill, New York 2008.
- V.V. Vazirani, Approximation Algorithms, Springer-Verlag, Berlin 2003.
- S. Even, Graph Algorithms, 2nd edition, Cambridge University Press, New York 2012.
- T.H. Cormen, C.E. Leiserson, R.L. Rivest and C. Stein, Introduction to Algorithms, MIT Press, Boston 2009.
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) (or equivalent courses) 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.
There will be six homework assignments, the midterm and final exam. The final grade will be based on the grade of homework assignments (30%), of the midterm (30%), and of the final exam (40%). The homework assignments will mainly contain questions of design and of analysis of algorithms, and typically will not contain programming tasks.
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.