Advanced Methods in Algorithms
Instructor: Vitaly Skachek
Teaching assistant: Pille Pullonen
Lecture: Wed. 14.15 - 16.00, J. Liivi 2-512
Practice: Fri. 12.15 - 14.00, J. Liivi 2-611
Office hours: TBA, J. Liivi 2-216 (or by appointment)
Contact: Vitaly Skachek, Pille Pullonen
- 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) before you take this course. 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 homeworks and the final exam. The final grade will be based on the grade of homeworks (60%) 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.
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.