Algorithms and Data Structures II
In the winter semester 2018/2019, I teach the English version of the basic course on Algorithms and Data Structures II [NTIN061]. It is primarily intended for students of the English study programs, but everybody is welcome.
The lectures are held on every Monday from 10:40 in room S4.
Classes (exercises) are on Mondays from 15:40 in room S11. They are taught by Matej Lieskovský. Czech-speaking students can also select any classes of the Czech version of the course — we will try to keep both versions synchronized.
If you want to contact me and consult anything, you are welcome to visit me in room S322 or to write me an e-mail to firstname.lastname@example.org.
|1. 10.||Searching in text: notation on strings, naïve algorithms, the KMP (Knuth, Morris, Pratt) algorithm and its analysis.|
|8. 10.||Text searching continued: Aho-Corasick algorithm searching for multiple strings simultaneously. Using rolling hash functions: the Rabin-Karp algorithm.|
|15. 10.||Network flows: Basic definitions and theorems on networks and flows. The Ford-Fulkerson algorithm, proof of its correcntess using cuts. Equality of maximum flow and minimum cut. Integer networks and integer flows. Reducing bipartite matching to integer flow.|
|22. 10.||Network flows: An equivalent definition of a flow. Layered networks and blocking flows. The Dinitz's algorithm.|
|29. 10.||Network flows: The Goldberg's algorithm (preflow push) and its analysis. Simulation: uniform path, bottleneck path, maximum height rule (source code).|
|5. 11.||Network flows: Goldberg's algorithm with the highest vertex rule. Multiplication of polynomials. A review of complex numbers.|
|12. 11.||Complex roots of unity. Fast Fourier transform and its inverse. FFT circuits, non-recursive FFT. Remarks on FFT (slides): algebraic interpretation, spectral analysis, signal processing.|
|19. 11.||Parallel programming on boolean circuits: binary addition. Introduction to comparator networks.|
|26. 11.||Comparator networks and bitonic sorting. Decision problems and reductions between them: SAT and 3-SAT.|
|3. 12.||More reductions: independent set, clique, 3,3-SAT, 3D-matching.|
|10. 12.||Complexity classes P and NP, NP-hard and NP-complete problems and their basic properties. Cook's theorem: SAT is NP-complete (proof sketched).|
|17. 12.||Plan: Fighting hard problems. Special cases: independent set in trees, coloring of interval graphs, pseudopolynomial algorithm for knapsack. Approximation algorithms: traveling salesman in a finite metric space (2-approximation), approximation scheme for knapsack.|
Recommended reading and other links
- Dasgupta, Papadimitriou, Vazirani: Algorithms (a beautiful books on algorithms covering the most of our lecture, available online)
- Cormen, Leiserson, Rivest, Stein: Introduction to Algorithms (2nd or later edition), Mc Graw Hill 2001
- Matoušek, Nešetřil: Invitation to Discrete Mathematics, Oxford University Press. (background in combinatorics and graph theory)
- Last year's lecture
- Other materials in Czech language