20602 - COMPUTER SCIENCE (ALGORITHMS)
Course taught in English
Go to class group/s: 31
Class-group lessons delivered on campus
To feel comfortable in this course you should have a good knowledge of calculus, statistics, probability theory and programming.
The course will teach the students the fundamentals of designing and analysing algorithms. The students will learn to apply design paradigm when designing their own algorithms and will be able to estimate the computational complexity and the resource requirements of algorithms they encounter. They will be familiarized with important algorithms and data structures and be able to use them as building blocks in their own work. They will also understand algorithms on graphs, randomized algorithms, optimization algorithms and the fundamentals of NP-completeness.
Introduction: Basic Notions and Theoretical Background
Introduction, Turing Machines
Stacks and Queues
Array Resizing, Analysis of Algorithms, Asymptotic Notation, Exercises
Programming Paradigms and Data Structures
Sorting, Comparison Sort Limits, Quicksort
Binary Heaps, Binary sort, Binary Queues
Binary Search Trees, Red-Black Trees
Shortest Path Algorithms
Dynamic Programming I
Dynamic Programming II
Algorithms for large scale data
- Approximation algorithms
- Linear Programming
- Simplex algorithm
- Interior point methods
- Network flow algorithms, max flow min cuts I
- Network flow algorithms, max flow min cuts II
- Online decision making I
- Online decision making II
- Randomized algorithms I
- Randomized algorithms II
- Understand the basic notions of algorithmic complexity, various design paradigms and data structures
- Develop an intuition about which problems are amenable to which kind of programming paradigm and relate this to common computational tasks like sorting and optimization
- Analyze the structure of advanced algorithmic schemes
- Understand optimization algorithms and the role of randomness
- Understand implications of NP-completeness
- Design algorithms using common paradigms and predict their scaling in terms of memory and computational resources
- Describe algorithms (possibliy developed by the students themselves) in pseudocode
- Read literature on algorithm design
- Develop algorithms for large scale difficult optimization problerms
- Show which problems cannot admit effiicient solutions
- Face-to-face 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 their own ideas. The questions will be about the presentation and related topics that were covered in class.
The exam will test the students' ability to explain algorithms using the concepts learned in class and connect these concepts to specific problem instances. It will further test if the student can describe the scaling properties of the presented algorithms in terms of the mathematical notions of complexity learned in class. Depending on the topic of the presentation, the abilities of the students in the design of algorithms will be assessed and the understanding of related topics from the course will be tested.
- T.H. CORMEN, C.E. LEISERSON, R.L. RIVEST, et al., Introduction to Algorithms, MIT, 3rd edition.
- R. SEDGEWICK., and K. WAYNE. Algorithms. Addison-wesley professional, 4th Edition.
- C. MOORE, S. MERTENS, The Nature of Computation, Oxford.
- R. MOTWANI, P. RAGHAVAN, Randomized algorithms, Cambridge University Press New York, NY, USA
- Bertsimas, Dimitris, and John N. Tsitsiklis. Introduction to linear optimization. Vol. 6. Belmont, MA: Athena Scientific, 1997
- Garey, Michael R., and David S. Johnson. Computers and intractability. Vol. 174. San Francisco: freeman, 1979.
- Lecture notes by the instructors.