20602 - COMPUTER SCIENCE (ALGORITHMS)

To feel comfortable in this course you should have a good knowledge of calculus, statistics, probability theory and programming.

Scope of the course is to provide the conceptual tools at the root of basic classes of optimization and sampling algorithms. These notions and method are extensively used in subsequent courses of the education program.

• Review of graph theory.
• Review of complexity theory and approximation schemes.
• Optimization algorithms: Linear Programming and integer Programming.
• Dynamic programming.
• Randomized algorithms for optimization.
• Monte Carlo Markov Chains for sampling and optimization.
• Stochastic programming, multi stage optimization.
• On-line algorithms over networks.

• Understand the basic notions of approximation algorithms.
• Analyze the structure of advanced algorithmic schemes for optimization and sampling.
• Illustrate the role of randomness in optimization.
• Master the basic notions of on-line algorithms.

• Develop algorithms for large scale difficult optimization problerms.

• Face-to-face lectures

Lectures.

The exam consists of a presentation and questions. The presentation can be either about a specific topic related to the course content, or about a project that the students complete before the exam. Several possible topics and projects will be proposed and students can also suggest also their own ideas. The questions will be about the presentation and related topics that were covered in class.

• T.H. CORMEN, C.E. LEISERSON, R.L. RIVEST, et al., Introduction to Algorithms, MIT, 3rd edition.
• C. MOORE, S. MERTENS, The Nature of Computation, Oxford.
• R. MOTWANI, P. RAGHAVAN, Randomized algorithms, Cambridge University Press New York, NY, USA.
• D. BERTSEKAS, Nonlinear programming, Athena Scientific, 3rd edition.
• Lecture notes by the instructors.