Advanced algorithms (2006/2007)

Learning outcomes

The goal of this course is to introduce some advanced paradigms for algorithms development and analysis in order to solve optimization problems.

Main concepts recall about computational problems: definition, instances, encoding, precise and approximate models. Optimization computational problem.

Main concepts recall about algorithms: computational resources, input encoding, input size/cost, computational time. Worst and average analysis. Computational time and growth order.

Computational time vs. hardware improvements: main relations. Efficient algorithms and tractable problems.

Divide et impera paradigm
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Definition and application to some problems.

Greedy paradigm
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Definition and application to some problems. Matroids and greedy algorithms.

Backtracking technique
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Definition and application to some problems.

Branch & Bound technique
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Definition and application to some problems.

Dynamic programming paradigm
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Definition and application to some problems.
Memoization and Dynamic programming.

Local search tecnique
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Definition and application to some problems.

Approximations algorithms
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Definition and some application examples.
Simulated annealing.
Tabù search.

Probabilistic algorithms
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Definition and few application examples.
Numerical probabilistic algorithms, Monte Carlo algorithms and Las Vegas algorithms. Examples: Buffon's needle, Pattern Matching and Universal hashing.

Quantum algorithms
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Introduction to qubit, quantum state concepts. Information coding by qubits. Quantum algorithms. One example of quantum algorithm: Fourier Quantum Transform.

The final exam consists of a written part followed, if it is sufficient, by an oral part.