Problems and Algorithms

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Code Completion Credits Range Language
MI-PAA Z,ZK 5 2P+1R+1C Czech
Garant předmětu:
Department of Digital Design

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.


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

Syllabus of lectures:

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

2. Models of computation. The classes P and NP. Polynomial hierarchy.

3. The notion of completeness. Complexity comparison techniques. The classes NP-complete, NP-hard and NPI.

4. The classes PO and NPO and their structure. Deterministic approximation algorithms. Classification of approximative problems. Pseudopolynomial algorithms. Randomization and randomized algorithms.

5. Communication and circuit complexity

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

7. Local methods: state space and search space, exact methods, heuristics.

8. Simulated annealing.

9. Simulated evolution: taxonomy, genetic algorithms.

10. Advanced genetic algorithms: competent GA, fast messy GA, Stochastic optimization: models and applications. Bayesian optimization.

11. Tabu search.

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

13. Reserved

Syllabus of tutorials:

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.

Study Objective:

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.

Study materials:

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.

Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-04-13
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