Problems and Algorithms

Přednášející:

Petr Fišer (gar.)

Cvičící:

Petr Fišer (gar.)

Předmět zajišťuje:

katedra číslicového návrhu

Anotace:

Students are able to evaluate discrete problems by complexity and by the purpose of optimisation (on-line tasks, multicriterial optimisation). They understand principles and properties of heuristics and exact algorithms and, therefore, are able to select, apply, and experimentally evaluate a suitable heuristics for a practical problem.

Požadavky:

The notion of complexity, asymptotic complexity bounds. Basic graph theory. Programming in any imperative language using queues, stacks, and lists.

Osnova přednášek:

1. Discrete optimization, examples of practical tasks. Combinatorial problems. Algorithm complexity, problem complexity.

2. State, state space, search space. Basic exact search methods.

3. Decidable problems. models of computation. The classes P and NP. Polynomial hierarchy. The classes PO and NPO.

4. The notion of completeness. Complexity comparison techniques. The classes NP-complete and NP-hard. The structure of NP and NPO.

5. Deterministic approximation algorithms. Classification of approximative problems. Pseudopolynomial algorithms. Randomization and randomized algorithms.

6. Practical deployment of heuristic and exact algorithms. Experimental evaluation.

7. Simple local heuristics in state space and search space.

8. Simulated annealing.

9. Simulated evolution: taxonomy, genetic algorithms.

10. Advanced genetic algorithms: competent GA, fast messy GA, the selfish gene method. Applications to multicriterial optimization.

11. Stochastic optimization: models and applications. Bayesian optimization.

12. Tabu search.

13. Global methods, taxonomy of decomposition-based methods. Exact and heuristic global methods, the Davis-Putnam procedure seen as a global method.

Osnova cvičení:

1. Seminar: terminology, examples of complexity.

2. Seminar: examples of state space.

3. Homework consultation when required, self-study: dynamic programming revision.

4. Solved problems session: the classes P and NP, complexity proofs, problems beyond NP.

5. Solved problems session: completeness, reductions.

6. Homework consultation when required.

7. Homework consultation when required.

8. Homework consultation when required.

9. Midterm test.

10. Homework consultation when required.

11. Solved problems session: advanced heuristics, applications.

12. Homework consultation when required.

13. Homework consultation when required.

14. Backup test term, evaluation.

Cíle studia:

Many practical tasks are computationally infeasible. Students will learn to distinguish tasks where the complexity grows too fast with the task size from those which are undecidable independently of size. They will learn fast algorithms for exact and, primarily, approximate solution. Some of the more advanced ones are inspired by processes in nature and sometimes referred to as softcomputing. A series of homeworks will lead students from very simple tasks to applications of advanced heuristics on a practical problem.

Studijní materiály:

1. Garey, M. R., Johnson, D. S. ''Computers and Intractability: A Guide to the Theory of NP-Completeness''. W. H. Freeman, 1979. ISBN 0716710455.

2. Ausiello, G., Crescenzi, P., Kann, V., Gambosi, G., Spaccamela, A. M. ''Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties''. Springer, 2003. ISBN 3540654313.

Poznámka:

Rozsah=prednasky+proseminare+cviceni2p+1r+1c, Prednasejici: Ing. Jan Schmidt Ph.D.

Rozvrh na zimní semestr 2011/2012:

Rozvrh není připraven

Rozvrh na letní semestr 2011/2012:

Rozvrh není připraven

Předmět je součástí následujících studijních plánů:

• Computer Security, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět oboru)
• Design of Digital Systems, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět oboru)
• Computer Systems and Networks, Presented in English, for Students, who Enrolled in 2010 and 2011 (povinný předmět oboru)
• Information Systems and Management, in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět oboru)
• Software Engineering, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět oboru)
• Web Engineering, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět oboru)
• Knowledge Engineering, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět oboru)
• Master Informatics, Presented in English - Version for Students who Enrolled in 2010 (VO)
• Master Informatics, Presented in English - Version for Students who Enrolled in 2011 (VO)
• Master Informatics, Presented in English - Version for Students who Enrolled in 2012 (VO)
• Computer Security, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět oboru)
• Information Systems and Management, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět oboru)
• Software Engineering, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět oboru)
• Web Engineering, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět oboru)
• Knowledge Engineering, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět oboru)
• Design of Digital Systems, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět oboru)
• Computer Systems and Networks, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět oboru)